The Fit Acceptance Testing Framework
Fit ("Framework for Integrated Testing"), also often spelled FIT is the engine that actually processes each FitNesse test table, using the FixtureCode referred to by that table. The idea of test tables, and the set of TestTableStyles, come from Fit.
FitNesse is an HTML and wiki "front-end" to Fit. While Fit makes it possible to run test tables, it does not itself provide an easy means of creating those tables or displaying the results of those tests. This is where FitNesse comes in. FitNesse makes it really easy to create, run, organize, annotate, and share Fit tests throughout a software development team.
Interestingly both the wiki and Fit were developed by Ward Cunningham, and you can read about them both on Ward's c2 wiki.
Throughout this User Guide, when we talk about how test tables are run, we often talk about Fit, since it is in fact doing the work. But for your purposes as a FitNesse user, Fit is just part of the magic: FitNesse hides Fit from you completely. You really don't need to worry about it at all.