1. An ace-high straight, e.g., 10♥J♦Q♠K♣A♥. It's the best straight possible, but it's not always the best hand possible since flushes, full houses, quads, straight flushes, and royal flushes still beat a Broadway straight.
2. An adjective referring to cards ranked 10x through Ax Thus, a "Broadway hand" would be one containing any two Broadway cards, such as K♠J♦.
The Broadway term to indicate high cards and the highest possible straight comes from the famous Broadway in Manhattan, New York. The reference alludes to the length and popularity of the New York street with its high-end buildings and many famous theaters.