Definition of broadway
There are 20 broadway in a regular deck of 52 cards. The broadway's are the four tens and all tricks (jacks, queens, kings, aces). When we talk about a player who plays all broadwayss, we are talking about a player who plays any combination of these 20 cards (KT, KJ, KQ, QJ, etc). When someone makes a straight with T-J-Q-K-A, we're talking about a straight broadway. The best possible poker hand, the straight flush (royal straight flush) is also a straight broadway.
Reference to the expression broadway
The expression broadway in poker refers to high cards. The term broadway comes from the famous Manhattan boardwalk, broadway in fact. This promenade is very popular (as are the broadway cards) and there are several very high towers and several theaters.