The “hook” button (sometimes “hook/flash”, “flash” or “recall”) on a fax machine or telephone simulates hanging up the line, even if the fax machine is still active or the phone receiver is off phone.
What it “hook” is used for
The hook button button is used to hang up the line, other times it is used (as a quick press) to switch to a call waiting on the same line.
Origin of the term
The term likely originates from the hook that a telephone handset hung on in older landline phones.