Definition of broadway
There are 20 broadways in a regular 52-card deck. The broadways are the four tens and all the tricks (jacks, queens, kings, aces). When we talk about a player playing all his broadways, 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, it is called a broadway straight. The best possible poker hand, the royal straight flush, is also a broadway straight.
Reference of the expression broadway
The term broadway in poker refers to high cards. The term broaday comes from the famous boardwalk in Manhattan, the Broadway. This boardwalk is very popular (as are the broadway cards) and there are several very tall towers and theaters.