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 SpotPass 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).
Dread Fighters and Brides still function as normal if the player has not unlocked them yet, the only difference being that they have a Tactician model instead. Any DLC skills they carry work as normal, although the player will not know what ability it is until they have unlocked it themselves.
If the other team's Avatar is of a Dread Fighter or Bride class, they will be unable to recruit them if the player has not unlocked the class yet.
In the American and European releases there is currently a glitch that will send out a random team if you use downloadable map characters or items. 
When two players have StreetPass activated and exchange data, 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 items off the other team, depending on what the team is carrying. If they are carrying Forged weapons, the forge cost is stacked along with the weapon's original price. The forge cost is not halved by the effects of the Silver Card. Unique weaponry (e.g Excalibur, Ragnell), cannot be bought from the team if they are carrying it, the only way to get more of these weapons is through the DLC Infinite Regalia.
The player can also check the team's stat totals, the items that they are carrying and their skill sets. They may also buy the leader for half price (this cost is not lowered through the Silver Card), who will then join the player's team with no items. This is good when doing Classic mode to replace any other lost members (best for any lost SpotPass members, since they do not help well in Pair Ups). If they die in battle, you will have to pay double to recruit them from the Avatar's Logbook or wait for their team to reappear on the World Map.
Like other SpotPass teams, buying any items or their leader will result in them leaving after you are done with your purchases.
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 player's settings. They are computer controlled and do not use Pair Ups and other dual-related functions, such as Dual Attack and Dual Guard. If the player's team routs the other player's team, they can recruit the leader for free.
My Castle Edit
In Fire Emblem Fates, Streetpass is used for My Castle battles, and function much like Streetpass battles in Awakening. Unlike in Awakening, where the other team's Avatar appears in a random location, the Avatar appears in a small localized area in the player's castle. The player is allowed to visit another player's castle. If the player chooses to battle, they can either choose to battle in the opponent's castle or their own castle. If they choose to battle in the opponent's castle, they must either defeat the Streetpass team or seize the throne; if not, they must defeat the opponent's team and defend their throne. If the player wins, they are allowed to buy skills from a corresponding unit (such as Felicia buying Battle Command from an opposing Felicia) or they can buy an opposing unit.