21 was the age once upon a time when a person was officially considered an adult and they received the key to the door to signify that fact. Legally I think you'll find there are some things you still can't do until you turn 21 such run for MP.
The reason for the conference of 'adult' status at the age of 21 was linked to the age at which an individual could vote - which was 21, before it was reduced to 18. The 'key of the door' was a tradition denoting that the 'child' was now old enough to come and go as they pleased.