The term bet can be used in a few different ways, but generally means "agreed" or "okay". For example, if someone says "Wanna grab lunch later?" and the other person responds "Bet", it means they agree to the plan. Bet" can also be used as a response to confirm that a statement is true.
The slang bet is evidenced by the 1990s, recorded in a collection of campus slang (and likely popularized by Black popular culture). It was an early entry on Urban Dictionary in 2003 04. It's typically used as an exclamation: Bet! That has the sense of Excellent! or, to draw on a similar slang expression, Word!