A 'Round' is when everyone goes about their turn. Once everyone has used their turn in a round, another one starts and gives everyone a new turn to play with. So when you're on a waitlist and you're at 'start in 3 rounds' that means everyone not in the waitlist has gotta go through three turns each before you can finally play. Booile got through '1 round', getting him out of a waitlist, making him now able to start in 10 'turns'
So basically
Turn = the 5 seconds you get to move and shoot
Round = can't really explain other than it's literally just a round of turns. Everyone gets 1 turn in a round, then when everyone uses their turn, everyone gets their next turn to play and a new round starts