RobbieLad's description of a "finesse"

1. Your partner leads low,

2. Next player goes lowish or offsuit,

3. You have both the ace and the queen, and play the queen.

You stand a 2/3 chance (more or less) of winning the trick with the queen, hence keeping the ace for a further trick.

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Daffer's Addendum: Finesses work MUCH better with uncalled aces.

Another scenario:

1. You have both the ace (uncalled) and the queen, and you have the lead play the queen.

2. If your opponent in the second seat has the king s/he may hold back from playing it in hope that their partner has it or in fear that the other opponent has it.