What is the Meaning of the Expression
MAY I BE EXCUSED or CAN I BE EXCUSED?

Definition:

a polite question at the end of a meal asking the host/hostess for permission to leave the table

This is especially appropriate for children if they are asking to leave the table before the adults are prepared to leave.  e.g.,  If the adults have coffee after dinner, and the children want to leave to play, the children can ask to be excused.

Note:  “May I be excused?” or “May I please be excused?”  is the grammatically correct option.

“Can I be excused?” or “Can I please be excused?” although technically not correct, is common in informal conversation.

Examples:

1. Her grandson asked, “Can I be excused?

2. The children may be excused, if they want, to go outside and play.