Generally speaking, people refer to an application's presentation layer as its front end, its persistence layer (database, usually) as the back end, and anything between as middle tier. This set of ideas is often referred to as 3-tier architecture. They let you separate your application into more easily comprehensible (and testable!) chunks; you can also reuse lower-tier code more easily in higher tiers.
Which code is part of which tier is somewhat subjective; graphic designers tend to think of everything that isn't presentation as the back end, database people think of everything in front of the database as the front end, and so on.
Not all applications need to be separated out this way, though. It's certainly more work to have 3 separate sub-projects than it is to just open index.php and get cracking; depending on (1) how long you expect to have to maintain the app (2) how complex you expect the app to get, you may want to forgo the complexity.