In a JSON schema the format keyword has a number of pre-defined formats (date, email, etc.) but can also be any custom format (see 7. Semantic Validation with "format"). If you simply need a to match a field against a regular expression you should use the pattern keyword instead. Custom formats are intended for annotation and more complex validation that is not possible to accomplish with a regex.
A custom format has a title and a validation function that validates the string value of the field according to the rules of the format.
title - A user readable description of the format that is used to annotate the field.validation - A validation function (see etaque/elm-form for details on how to write a validation function).
A list of custom formats with a format identifier for each.