Felt paper is used in most roofing as a barrier between the two materials, wood and asphalt. Back in the day, wood planks where used as decking. This is where the shingles were nailed to. It was common for sap to leak from these boards and would break down the “backside” of the shingles causing them to deteriorate. This is no longer a concern as the decking is now OSB board (oriented strand board).
You can also think of it as an additional layer of protection. Say the wind blows off a shingle or tile in a storm, the felt paper will act as a layer of protection from the rain. Should this happen, you should call a roofing company right away as this will not protect the like your shingle or tile.