1. In a video game when the team is trash or they die and one of the team members has to put the team on his back and carry them to a win.
2. To put someone on your back and take them

A Carry is a hero in Dota or Dota 2 which is designed to grow stronger with every level. Carry heros are the ones who will "carry" the team with their kills. Other heros take over other functions so as supporter, healer, disabler, stunner and so on.

(gay slang) To carry the way. To carry the torch. To have all your ducks in a row, and lead us.

In Halo 2 and Halo 3, the action of winning on a team slayer game by getting more than 75% of the kills on your team because everyone else on your team sucks.

Usually occurs during matches of Social Slayer.

to insult, begin to insult

when someone disses you!

to insult the reputation or quality of something or someone.

Often used in the rhetorical formulation, "How you wanna carry?" which expresses confidence that the thing/person can't be insulted.

Probably originated in Southeast D.C.