Lookee what he can do! He wants a job!
The small thin rectangular pieces are Status Effects. Certain Heroes and Leaders apply these. Status Effects are noted by brackets  on the card that applies them.
The Current Wave markers are used by both players to track the current Wave. They can be placed next to the current Wave on the side of the board to track this.
The First and Second player markers track who is currently first and second player.
The larger pieces with the Leader symbol can be placed on top of the Hero side of your Leader to cover their Hero abilities so you can focus more on their Leader ability.
Thanks. That helps. I couldn't figure out the Leader squares. I think I was wondering more about the round tokens that have life on one side and completely different icons on the other side.