Recharge refers to the roll required for a creature to be able to use an ability.
For example, if a monster ability says “Recharge 5-6,” that means the monster rolls a d6 at the start of its turn. If the roll is a 5 or a 6, the monster regains the use of the ability.
Some monster abilities say “recharges after a short or long rest.” In these cases, the monster only regains the use of the ability after finishing a short or long rest.
Monster Manual, pg. 11