What is a round by round poker tournament?

Answer 1

If you are referring to the term "A round" in Poker the answer is the following:

A round is the term for a certain number of hands. Lets say there are 6 players on the table and the button (Dealer) is at player A's location. The button then moves with each hand to the next player (From player A to player B etc). Once the button reaches player A again, the round is finished and a new one starts.

Answer 2

A round by round poker tournament or a tournament in a "round by round stage" is a tournament where only 1 hand is being played at the same time.

When playing in a regular tournament when your tables hand ends, a new hand is being dealt immediately after the one that just ended.

In a round by round tournament or in a round by round stage in a tournament once your hand is finished you must wait for all the other tables in that tournament to end too, this guarantees that all tables play the same ammount of hands. A perfect example of a "round by round stage" in a tournament is right before the final table, or right before the "bubble". (The bubble is the last player to be eliminated without wining a prize.) This allows an exact overview of who gets eliminated when to determine possible prizes or elimination order.