In Call of Duty Ghosts, there are seven different perk categories. These are called Speed, Stealth, Resistance, Handling, Awareness, Equipment and Elite.

Speed Perks

Speed perks allow the player to move faster and aim faster etc.

Quickdraw gives you faster ADS. This basically means that the time it takes for you to aim down your sights will be reduced. Especially handy for close quarters combat.

Sleight of Hand
This perk allows you to quickly reload your weapon.

Faster movement speed. Basically, its kind of like Lightweight from previous games.

Marathon allows you to sprint for longer distances. If you've played COD before, you'll know that you character can only sprint for a certain number of seconds before slowing down. With Marathon, you don't have to worry about this. Often used by rushers and those playing objective-based game modes such as Capture the Flag.

Stalker allows you to move quickly while aiming down your sights.

Stealth Perks

Stealth Perks do exactly what you'd expect them to. Their primary role is to keep you from being noticed by other players.

Take Down
Take Down allows you to kill enemies without having to worry about them automatically telling players their location. Basically, it allows you to dispatch enemies in a silent fashion.

Blind Eye
Blind Eye makes you undetectable to all AI-controlled killstreaks. i.e. AI-controlled killstreaks will not target you (think of the Chopper in previous games).

Off The Grid
Off The Grid is the COD Ghosts version of Ghost / Assassin. Using this perk will make you invisible to enemy SAT-COMs. In case you didn't already know, SAT-COMs are ground-based UAVs that will show your position on the enemy player's minimap.

Dead Silence
Dead Silence quietens your footsteps so that enemy players can't hear you running up on them. Particularly popular among those who like to "sound whore" with headsets. Also seems to be used a lot in game modes such as Search and Destroy.

When you have Ghost equipped as one of your perks, the red name tag that usually appears above your head will be invisible to enemy players. The red crosshair will also fail to appear while they are aiming at your body.

Resistance Perks

The Resistance tier is focused on increasing your ability to withstand damage.

Lightweight will prevent you from taking fall damage. This means that you can jump off higher buildings and not have to worry about falling to your death.

Not entirely sure what this one is yet. Some have said that it gives you faster health regeneration. In previous games, Painkiller was a death streak that allowed to take a lot of bullet damage.

Toughness reduces the flinch that you experience whenever you take damage while aiming/shooting. This is a lot more useful than you think it is, as you'd be surprised how many gun fights are lost because of the effects of flinching.

Tac Resist
Tac Resist will make you resistant to enemy-thrown tactical grenades such as flash bangs and stun grenades.

Blast Shield
Blast Shield gives you increased resistance against explosive damage.

Handling Perks

The Handling Perks are focused on your hand work (duh).

Strong Arms
Strong Arms will allow you to throw equipment further than normal. i.e. You'll be able to toss lethal equipment such as C4 over further distances.

On The Go
On The Go allows you to reload while you are sprinting.

Fast Hands
Fast Hands will allow you to swap between weapons in a much quicker fashion. i.e. If you run out of ammo in your primary weapon, Fast Hands will allow you to swap to your secondary in the blink of an eye.

Steady Aim
The description of Steady Aim is still unconfirmed. In previous games, this allowed you to hold your breath for longer while aiming with a sniper. My guess is that it will stop your hands from shaking whenever you're holding your breath.

Dexterity will reduce the amount of time it takes you to draw your weapon after sprinting. If you've played COD before, you'll know that there is noticeable delay between the time it takes you to stop running and aim your weapon.

Awareness Perks

The Awareness Perks are focused on increasing your awareness of your surroundings and enemy players. Think of them as sixth senses.

Recon will paint enemy players on the minimap if you manage to give them explosive damage. For example, if I injure a player with a frag grenade or a "noob tube", that player will show up on the minimap for a predetermined period of time. This one is especially popular in Search and Destroy, where painting enemies on the radar can win you the round.

When you have Scavenger equipped, you will be able to see and pick up small ammo bags around fallen enemy soldiers. This is especially useful for those using weapons with a high rate of fire.

Sitrep will highlight enemy equipment and SATCOMs in red.

Awareness will increase your ability to hear enemy footsteps. In some of the previous games, this was a pro variant of Sitrep and it basically made enemy players sound like elephants.

Wiretap is kind of like Hacker in the sense that it allows you to use enemy SATCOMs as your own.

Equipment Perks

The Equipment tier is basically focused on giving you more equipment to use (i.e. two stun grenades instead of one, etc).

Tac +1
Tac +1 will give you an extra piece of tactical equipment. i.e. You'll be able to carry two flash bangs instead of one.

Lethal +1
Lethal +1 is basically the same thing as Tac +1. Only difference is that it will allow you to carry two pieces of lethal equipment instead. Example: 2 pieces of C4 instead of one.

Bandolier will give you extra magazines. i.e. You'll spawn with more ammo than normal.

Attachment +1
In COD Ghosts, weapons can be given three attachments. With Attachment +1, you'll be able to equip a fourth attachment.

Danger Close
Danger Close will give you the ability to deal out greater explosive damage.

Elite Perks

Elite Perks are kind of a mixed bunch.

Gamble will allow you to have two perks from the same tier / section. Some have said that it also allows you to reroll care packages.

Using Hardline means that all point streaks will require one less kill than they normally do.

Ping allows you to detect enemies that are nearby to enemy players that you've just killed. i.e. If you kill an enemy, then the radar / minimap will give you a quick "ping" and let you see the locations of enemy players that are close-by. Will be incredibly useful in Search.

Overkill gives you the ability to equip two primary weapons. Basically, you can equip an assault rifle as your primary and a sniper rifle as your secondary.

Dead Eye is a perk that increases the probability of "increased damage" the further you get into a pointsteak.