Everybody uses splitters on their telephone lines. If you want to connect up more than one telephone into the same socket, the chances are you're using a splitter. When you're connected via ADSL, you need a special type of splitter which contains a micro-filter.
There are two reasons why they're required. The first is to stop the ADSL signal interfering with the voice part of your phone line - this sounds a bit like 'fast clicks' when it happens. The second reason is to ensure that the ADSL line is terminated correctly. Without becoming too technical, an unmatched termination can cause reflections back down the line. This is a bad thing and can cause errors on your ADSL connection. The above graph shows the frequency range that your phone (POTS) and ADSL occupy. Don't worry if you don't understand because it's not all that important to the end user.
There are many splitters on the market and they come in different shapes and sizes. In most, if not all cases, the letters "ADSL" are printed somewhere on the device. A couple of examples including the original BT faceplate (centre) are shown in the picture below.