A rubber is a round of play in a card game. Bridge is played in "rubbers". Once a rubber has begun, one is obliged to play until it is finished, but then the players can be changed out.

For instance, when Elinor has been talking to Lucy there comes this bit: ...Elinor was soon called to the card-table by the conclusion of the first rubber... That means that one round of play had ended and Elinor was then brought in to replace a player and begin a new rubber.