An obligatory finesse occurs when declarer is "obliged" to duck an honor. For example:
Needing 3 tricks in the suit, you lead toward the king, which holds the trick. You continue with a low card from dummy, East playing low. At this point, you have an obligatory finesse. Play low from hand and hope that West started life with the doubleton ace.
A similar example needing 4 tricks:
You lead low to the queen, which wins. A spade back to hand should be ducked in case West began with the doubleton ace.