In the days of King Alfred, that is, in Old English, an imp was a sapling or offshoot of a tree.
This meaning gave rise to a figurative use, the scion of some noble house or, especially, a male child.
Then, in due course, probably because most male children are mischievous, imp became synonymous with a young demon. Thus since the sixteenth century an imp may be a mischievous child, a young demon, or one of the petty fiends of hell.
The original meaning has passed completely out of use.