Generally speaking, business professional (or just professional) refers to a suit and tie however it could also be a sports coat and slacks (with tie). The alternative, business casual, could be slacks and a button down shirt, or perhaps khakis and a polo shirt (this may be too casual depending on the circumstances). Obviously this can all vary depending on a variety of factors (where you are, what you're doing, etc..). In some places you could wear slacks, button down shirt, and a tie with no coat (sweater optional) and it could be considered business professional. In other places suit and tie is the only way to go.
As far as I know, vests are optional, but in my opinion it does make you look MORE professional. Guess its a matter of whether you're just trying to abide by the rules or make yourself look good.