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 the phone.
It more often used to open a line for a dial tone.
The hook 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.
It is more commonly used to open a line for a dial tone. When you press the hook button, the fax machine simulates taking a phone handset off the phone line. Often there is a dial tone played over a speaker. From here, you can dial a fax number as a regular phone number would.
This feature is useful when there are odd numbers to dial, an extension to get outside of a corporate network (such as dialing ‘7’ or ‘9’ before the fax number), or when the destination fax number has an extension that needs to be dialed after the number connects.
Once the fax tone on the other end starts, you will need to press the “send” button to start the fax process.
The term likely originates from the hook that a telephone handset hung on in older landline phones.