It's an Invasion!

Garrison Invasions are challenges in your Garrison that allow you to defeat attacking enemies for rewards.
They can be completed solo but you are encouraged to bring your friends because the rewards are greater if you perform better.
Your first invasion comes early on Shadowmoon Valley and Frostfire Ridge with a Tier 2 Garrison--midway through questing, a player's Garrison will be attacked either by a Thunderlord or Shadowmoon force. This is not available with a Tier 3 Garrison but it is also not considered a "real" invasion.

There are 6 types of invasion:
Ogre
Shadow Concul
Shadowmoon
Botani
Goren
Iron Horde

HOW TO TRIGGER AN INVASION
When you kill level 100 mobs (in the areas for Apexis Crystal Quests), you have a chance that the enemies will prepare to attack your garrison in retaliation. At this point, your commander by the Town Hall will have a quest for you.

In order to trigger an invasion, you will need to kill mobs at following locations:
http://i.imgur.com/RVKLBzR.jpg

Note that you need to kill approx 500 mobs, and you can not be in the raid group. Party is allowed.
Once you kill enough of them, you will get notification at your minimap, where you can see mission status. There will also be big yellow exclamation mark there, pretty easy to spot. Once you spot it, head back to your garrison and you will be able to take quest from Sergeant Crowler (A) or Sergeant Grimjaw (H).

Invasion Stages
The invasion has the following stages:
Invasion - Follow the sergeant
Assault - defeat the assault.
The holdout - endure the assault. This part is timed for ~8 minutes.
The calm - go to the town center
Final stage - kill a boss

During the assault, multiple enemy packs spawn in your Garrison.The following unusual things can happen as well:
The enemy assaults a Garrison building—attack them to interrupt the cast.
A terrified townsfolk runs out of safety. They are marked with a green arrow over their head and you run up to them to move them away.
An infiltrator from the opposite faction is in your Garrison. These have a hefty bit of HP.

Invasion Points
During the invasion, you gain points via the following ways:
Killing enemies—trickier ones give more points.
Saving terrified townsfolk.
Killing spies.
Keeping your buildings intact.
Keeping your defenders alive.
Killing the final boss.
When the invasion is complete, points are added for your buildings and defenders.

You need 300 points for Bronze, 600 for Silver, and 1000 for Gold.

Invasion rewards
Silver and bronze rankings rewards only apexis crystals, but if you managed to get gold reward you will get Invader's Forgotten Treasure which can contain 645 items (They can be warforged 651) and one of 4 mounts.
Note that you can get each bag just once per week, yet you will receive apexis each time you do it.

Good luck with invasions!

According to a recent blue post, invasions are supposed to happen "Organically" which mainly entails doing the apexis dailies that pit you against any of the factions that could invade your garrison. Killing mobs in the daily areas will give progress towards this, as well as a sizable increase when you finish a daily quest (I'm not 100% on this, but it's the most logical option)

When you get an invasion triggered, you'll have a notification pop up by your garrison button on the minimap informing you of the invasion. Don't be alarmed, you can return to your garrison at any time you choose without risking the invasion starting when you arrive, as you must manually start the invasion when you return.

Invasions are graded on a point scale, with the rankings being Bronze (300), Silver (600), or Gold (1000), with points being divvied up for each kill and for some bonuses at the end based on structures not burned down and total number of living defenders (NPCs). When my group of 3 finished the timed wave, we had roughly 890 points, and the bonuses put us over 1000 for the gold. I'm not sure if the boss actually gave points upon defeat, but it seems a little tight for the point requirement with lower gear at the moment.

Editing this to add in an additional bit of knowledge

Some large buildings appear to have invasion benefits attached to them, for instance the Mage Tower let's you use Amperial Constructs to create a 2 way portal (Much like demonic gateway from locks) with a max range of 100 yards while the barracks allows you to set a rally point for a few extra npc guards. You may also ask a follower to come on patrol with you before starting your invasion to help out, they are a fairly significant damage increase!

How nice of the invading army to wait until the garrison commander is back!