The functional specification answers the requirements specification: the contractor describes how the requirements will be met, with what, and how they will be tested. Once agreed with the client, it is the common basis for development and acceptance.
The template holds the usual sections: summary and scope, solution concept, a table from every requirement to its implementation and test case, architecture and technology, testing and acceptance, schedule and open points. Every section has a short note and every table an example row. The Word file is for filling in and passing on, the Excel file has each section on a sheet of its own, and the PDF is for printing, for example for the review with the client.
No requirements specification yet? Start with the requirements specification template, where the functional specification picks up.