Want to know more about Latias in the game? This is the page for you.
Each Pokémon has base stats that determine how powerful it is. These stats go on to influence many other aspects of a Pokémon's capabilities. Latias's base stats are as follows:
Special Attack: 110
Special Defense: 130
Special Attack: 140
Special Defense: 150
As a Legendary Pokémon, Latias has very good stats. She's more defensively oriented than Latios, whose stats veer more towards attacking, but that doesn't mean Latias can't attack — in fact, she can be quite good at it if you build a set for it. You can learn more about how to use Latias over in the strategy section.
Latias only has one ability, Levitate. This ability makes her immune to Ground-type moves. It also makes her immune to most arena moves, such as Spikes, Toxic Spikes, Misty Terrain, Eletric Terrain, and Arena Trap. It's a good ability, and it makes sense given she's never shown on the ground; she can fly and is a psychic-type, so she can obviously levitate.
That said, Levitate isn't a perfect defense against Ground-type attacks — there are multiple ways to negate its effects. Pokémon with the ability Mold Breaker (which ignores the effects of abilities) will be able to hit Latias with Ground-type attacks. Zekrom, Reshriman, and White and Black Kyurem also all have abilities that negate Levitate. The hold item Iron Ball will negate Levitate as well.
The attack Smack Down knocks Latias out of Levitate, and this effect lasts until Latias switches out. The move Gravity also negates Levitate for five turns.
Gen VI introduced Mega Evolution, and it wasn't really a surprise that Latios and Latias were chosen as Pokémon to get Mega Evolutions. The one gripe I have is that their mega forms look nearly identical to me; I can barely tell them apart. I like the purple, don't get me wrong, I just have to look closely to tell them apart.
Anyway, Mega Evolution is pretty simple: it's basically a powerup for a Pokémon in the middle of a battle. It's not permanent evolution, just a temporary boost of power. It certainly adds a new dynamic to battling; it's a lot of fun. In order to Mega Evolve a Pokémon, you need to be far enough along in the plot of the game and you need that particular Pokémon's Mega Stone. In Latias's case, you receive a Latiasite as soon as you get it in Alpha Sapphire, whereas in Omega Ruby you'll receive it from your Pokémom after finishing the Delta Episode.
Mega Latias has a secondary purpose in Gen VI: the Soar mechanic. Using the Eon Flute, a key item given to you after catching Groudon or Kyogre, you can soar around Hoenn on Mega Latias's back. It is exactly as awesome as it sounds. What's more, Soaring opens up Mirage Spots, a retooling of the original games' Mirage Island. The Mirage Spots give you a ton of new areas with Pokémon from other regions to catch, as well as legendaries from the other games. Bulbapedia and Serebii have full breakdowns of everything you can do with it.
Latias and Latios have a special hold item: the Soul Dew. This item raises their Special Attack and Special Defense 50% when held. For obvious reasons, it's banned in official tournaments, and if you try to use it in tournaments within the game (e.g. the Battle Tower/Frontier/Maison) it won't work.
Getting the Soul Dew can be as difficult as getting Latias, because in most generations it requires the Eon Ticket. In Gen III you'll get it from the Eon Pokémon that's hanging out on the Southern Island. In Gen IV, the Soul Dew is the Engima Stone, which was a limited-time download item. In Black 2 and White 2, it will appear right next to where you catch Latios or Latias. Finally, in Gen VI, it's again held by the Eon Pokémon waiting on Southern Island.
There are many good move lists out there for Latias, so I won't bother copying one here. I personally recommend veekun for the many options it has. You can find a link to Latias at other Pokédexes at the bottom of that page.
Worth mentioning is that Latias has a unique move, Mist Ball, not learned by any other Pokémon. It's a Psychic-type attack dealing special damage with a base power of 70 and accuracy of 100%, with pp of 5. It has a 50% chance of lowering the target's Special Attack.