@allenJo - Well, you got it right the first time when you said that they were filters. They are both filters and splitters.
You may not need to split the home telephone wiring everywhere, but every phone plug needs the filter’s functionality.
What the filter does is eliminate a lot of the high frequency noise. You need to do this everywhere you have a phone jack; otherwise it will affect the quality of your DSL signal as well as the quality of your phone calls.
Yes, it seems a little counter-intuitive to have these filters sticking out of your phone jacks with nothing attached to them, but that’s just what you have to do. I don’t claim to understand the technology completely myself either.