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.
A "draw no bet" or "tie no bet" in soccer betting is just what it sounds like you're betting a team to win, and if it ends in a draw, your bet will be refunded. This is a popular way to back a team with a bit of a safety net, albeit at a worse price than you'd get on the regular three-way line that includes a draw.
