This is a question someone asked me yesterday and if you think about it, this is really a good question.
The partitioning function defines on which partition the row will be mapped based on the partitioning column value. Imagine that you have a table on which you have defined partitioning to make all rows with RecordType 1 to go to the PRIMARY filegroup and those with RecordType 2 to the ACTIVEDATA filegroup. How do we handle updates that change the RecordType from 1 to 2? The record obviously physically needs to move to the ACTIVEDATA filegroup but we are not inserting new data, we are just updating an existing row which has already been placed on PRIMARY.
Internally we are actually doing this by using a DELETE-INSERT operation. The 'old' row is deleted and the row with updated values is inserted and thus using the partitioning function to decide the physical placement of the row.
This is actually the same as with clustered indexes, when the value of your clustering key changes it might well be possible that its location in the table needs to change too and this is done in exactly the same manner.
--Clustered key update
--Partitioning key update