StreetPass is a feature available in the Nintendo 3DS. When enabled, it can allow two Nintendo 3DS systems to connect with each other and exchange data. While data is usually exchanged between a game feature called "StreetPass Mii Plaza", data can be exchanged for 3DS games, like Fire Emblem: Awakening.
In order to start a StreetPass, players must first create a StreetPass team, called My Team, consisting of 9 characters from their current roster and the Avatar, totaling 10 characters. These teams can be changed at any point and lock to your character's current Class, Stats, Skills, and weapons until you update them yourself.
There is only one StreetPass team that gets sent out per SD card.
DLC and StreetPass characters can be put onto your StreetPass team. If the other 3DS doesn't have the download content available, DLC skills still work save a few minor details (the icon in the skill window is a question mark, and they cannot obtain the DLC skill by recruiting your character).
DLC classes (Dread/Bride) work similarly in that they continue to function regardless though they appear as "Outrealm Class" and use the Tactician as their model. A unit of "Outrealm Class" cannot be recruited or added to the logbook of a player who doesn't have the appropriate DLC.
In the American release there is currently a glitch that will send out a random team if you use downloadable map characters or items. 
When a two players StreetPass exchanges data their teams will be exchanged. The team data received will appear on the Map as a Green Unit. Players can interact with these Units by buying an item in that Avatar's shop, scout the Avatar, or battle the Avatar's Team, similar to the function of SpotPass.
From the Avatar's shop, players can buy weapons and items that that Avatar's team is currently holding in their character inventories. This includes Forged Weapons which will be adjusted with the Forge costs. Legendary weapons such as Ragnell and Book of Naga will not be able to be sold in these shops.
Recruit allows the player to hire the other player's Avatar for a fee.The price of the Avatar is dependent on the current stats of that Avatar and the skills they have acquired. This can allow the player to make up for lost units in Classic Mode and will permanently stay in your party until they are defeated. You can re-recruit them if you StreetPass them again.
Battle obviously allows you to battle the other player's team. The teams are computer controlled and the difficulty of the battle is dependent on the other player's difficulty setting. They will not use the Pair Up function. If the player defeats the other player's My Team, the player can hire the other player's Avatar for free.