"Foil" is a mnemonic device that many people learn to help them remember the 'formula' for multiplying binomials. There are other ways of remembering the steps for multiplying binomials but this formula is probably the most commonly taught one.
The FOIL 'formula' is a way to multiply binomials. "FOIL" is an acronym to remember a set of rules to perform this multiplication. To FOIL you multiply together each of the following below
and then you add each of these products as demonstrated in the examples below.