Stats and Skills Breakdown:

You have a total of 6 primary stats. These stats determine your general physical prowess and intelligence, etc. Basically: if you ignore these even with high skills you won't get very far!

Strength - Your overall physical strength. How much can you bench, etc. This affects your ability with melee weapons as well.

Dexterity - This represents your ability to not only be accurate but also how quick you are. Things like firearms, dodging on foot and such fall under here.

Endurance - How much punishment you can take. Endurance affects your ability to block attacks and the like. For pilots and such it also plays into your ability to perform high-g maneuvers and knowing how to roll with strikes.

Intelligence - Are you smarter than a 5th grader? If you are, best make sure your INT stat is similarly up to snuff! This is your general level of education as well as how quick a thinker you are.

Spirit - This is a mix of both willpower and charisma. Spirit is invaluable to performers. The higher your spirit the more compelling your performance. This stat also affects your spiritia pool.

Luck - Luck affects every stat, so it can either be your best friend (Isamu Dyson), or your worst enemy (Hayao Kakizaki). Luck is the only stat that you don't get to pick where it starts out at.

Combat Skills:

These are your general combat abilities from handling weapons, to evasion. Please note: these skills are in general only for your capabilities on your own, not when piloting a VF or such.

Defense - This is your ability to take a hit and mitigate the damage (see: rolling with it).
Dodging - Your ability to actually evade attacks. Please put away the shades, Neo.
Firearms - This skill is geared towards most small arms (pistols, rifles, etc.).
Hand to Hand - Brawling, martial arts, etc. If your abilities include, er, 'expressing your true self' through your fists then this is your skill.
Heavy Weapons - This is for the big stuff. RPGs, light machine guns and so forth. No, baka mallets don't count.
Melee Weapons - Knives, swords, staves, anything that has a limited range plays into here. No, baka mallets still do not count.

Movement Skills:

These fellas play into your general ability to get around. So bear that in mind when you're trying to chase down that bus you just missed.

Climbing - Your ability to scale vertical surfaces, also plays in with things like rope climbing and dramatically holding onto someone while hanging off a cliff edge.
Running - This is what happens when you press the L and R buttons in most RPGs. Too low and the monsters will catch u- ...what's that? Wrong franchise? Oh, sorry. Point still stands though!
Leaping - Whether its standing in place or a running start, this is your ability to jump. However if your Endurance is too low, no you can't break that brick ceiling with your head.
Concealment - Contrary to popular belief, simply donning a skin-tight black suit that rides up uncomfortably does not make you a good secret agent. You need some points in Stealth for that.

Vehicle Operation Skills:

Ah, now this is probably the part many of you were looking for. Every skill in here is oriented around a vehicle of some kind, be it a car, tank, VF, or space ship.

Driving - Your skill in driving anything that stays on the ground. Are YOU a demon on wheels?
Navigation - Your ability to use maps, stars, terrain, etc. to figure out where you are. Jumping though Fold Space isn't like dusting crops, boy!
Electronic Warfare - Your skill in interpreting information from a craft's sensors. Don't take your eyes off that monitor!
Piloting - VFs, bombers, helicopters. If something flies this is the skill you need to use it. It's also useful in charming singers into making songs about you.
Star Ship Operation - It's a trap! ... Well actually it's your skill at managing the various systems that make a space ship work.
Gunnery - This is your skill in using a vehicle's weapons, be it missiles, gun pod, or a Macross Cannon. Incidentally: Missing with a Macross Cannon will result in a long term mocking at your expense.

Information Skills:

These skills represent your ability to get information from a variety of means. Not having any points in these doesn't make you an idiot. It only means you'll be about as ignorant as Basara Nekki.

History - This is your general knowledge of your race's history. Remember: You don't stand here because of the path that lies before you, but the path that lies behind you.
Interplanetary History - This would be how well versed you are in what has happened to other races. There's two things I can't stand: people intolerant of other people's cultures, and the Dutch.
Languages - In general it's assumed you can speak your native tongue, so this deals with your ability to speak other languages. You are only allowed to speak 1337 if this skill is maxed.
Politics - Not only your ability to grapple in the political arena, this plays a part in your ability to manage a crowd... And possibly whip them into a frenzy. No you may not shoot lightning at anyone who disagrees with you.
Gossip - An ear to the ground and a mouth wide open to spill out everything the ear picks up. Gossip generally deals with NPC contacts and finding out all the juicy tidbits they have. It's like high school all over again.
Streetwise - Similar to gossip, streetwise handles the seedier side of life. Just remember: if the Don does you a favor, he may one day call on you to do one in turn for him.

Performance Skills:

The other staple of Macross. This deals with your ability to wow the crowd and flaunt your stuff. Be warned, the ghost of Simon Cowell haunts the Horizon fleet's Miss Macross contest.

Singing - Kinda self explanatory, really. This is your vocal talent. Can you make that mountain move?
Musical Instruments - This covers your ability to play a musical instrument, generally associated with just one, multiple instrument specialties can be asked for. You'll need to be fairly good if you want to fly a jet with a guitar.
Dancing - You can't just stand around on stage, you gotta move to keep 'em interested! This skill also protects you against getting served.
Acting - When the spotlight hits, this skill determines how well you can slip into character. Just remember: you only need to think of the saddest moment in your life.
Advertising - Maybe you aren't as gifted as others, but you want to give them a leg up. This is the skill for the all-important manager.

Spiritia Skills:

This'd be the closest thing to magic in Macross. Spiritia is generally limited only to performers and Protodevilin. Performers will need a 7 in either Musical Instruments or Singing in order to be eligible for Spiritia skills. Furthermore in order to use them they will need access to SES equipment like the SES pack in order to be able to use these skills.

Attack - This skill is your ability to project your spiritia offensively, either damaging a target physically, or damaging their spiritia reserves.
Generation - Your ability to actually generate spiritia. This skill is only available for musicians and the like.
Sheild - Total opposite of spirita attack. This is the ability to use your spiritia defensively, typically as a barrier or such.
Absorption - Macross has vampires, but not in the Dracula sense. This is your ability to drain someone's spirita pool. This ability is for Protodevilin only.
Healing - Your ability to use your spiritia reserves to heal someone (organics only). For when the Black Mage casts the spells that makes the peoples fall down... Or something like that.
Enhance - Sometimes natural just isn't enough. Your ability to temporarily bolster another person's abilities. Disclaimer: The Administration of Macross: New Horizon do not endorse the use of performance enhancing drugs!

Specialty Skills:

Specialty skills deal with items that generally didn't fit well into the other areas. They cover a relatively broad scope and are especially useful to look at for people interested in playing support characters.

Computers - This covers everything from how to turn on a computer, to hacking systems, to coding an AI. As a note: kidnapping a virtual idol isn't crafty, it's creepy as hell.
Security - This skill largely deals with your ability to keep things safe and pick up on something trying to be slipped past you. An intelligent guard... Never would have seen that one coming.
Infiltration - While Stealth deals with being unseen, this skill has to deal with actually circumventing security systems, be they electrical of physical. You are quite skilled at avoiding traps. Either you are very cautious, or you are a coward!
Mechanical - If you're the sort who likes to work on machinery and patch things up then this is the skill you're looking for.
Medical - Your ability to diagnose and treat problems of the organic kind. Damnit Jim! I'm a doctor, not another bad joke!
Pickpocketing - The name is kinda self explanatory, really. If you fancy yourself the thieving kind then this is right up your alley. Just be careful you don't get your hand cut off!
Gambling - Your ability to tell when to place a bet, and even read a person's "tells". If you're good enough it can be viewed as another form of robbery.
Artistry - For the person who simply likes to build and design things. Also a skill for the disciples of Bob Ross.
Cooking - Hey, everybody has to eat, right? Good food can make all the difference in the world, and if some anime's are to be believed can even change the course of history (No really, it can't).
Fishing - A total joke stat, put here for the sole purpose of "because we can", but hey if you can find a good use for it then by all means!