Let's say you start with an Oracle database called PROD, replicated to a physical standby called STNDBY. You refresh your development environment by taking a copy of STNDBY via RMAN† and calling it MASTER. You open MASTER read-write, to do some actions (e.g. deleting sensitive user data) and then copy that for your developers, called DEV1, DEV2 etc. One of your developers wants to do some experiments, so he further clones DEV1 into DEV1A. So there are now many versions of our database, e.g
------ -------- -------- ------ -------
|PROD| -> |STNDBY| -*-> |MASTER| -*-> |DEV1| -*-> |DEV1A|
------ -------- -------- ------ -------
The * indicates points at which you have done OPEN RESETLOGS or created a new controlfile. This means a new incarnation of the database. You could not apply redo logs "backwards" in this chain, e.g. even if you shut down PROD (so its SCN does not increment) before creating MASTER, you could not make changes in a downstream database, for example DEV1, then apply the redo logs back to PROD even tho' they are the "same" DBFs - the incarnation has been incremented.
† this is what it means by recover backups from a prior incarnation