= Have sex
with him/her/it.
An
expression used to declare one's desire to have coitus with someone, coming from the verb 'Tap', which, in this context, is similar and related to screw, i.e. to put a thread on a piece of metal, or to insert said screw into a
receptive orifice.
'That' replaces 'him' or 'her', suggesting the receiver of the screwing is just an object, to be sexually used and then cast aside.