Put very briefly, with ADSL (ie broadband for most people), the digital side of the system is at a frequency much higher than audio. The audio band is essentially from 0 to 4 kHz (4000 cycles per second). Anything higher than that is likely to be the broadband part. The microfilters just block that part of the signal out so that it doesn't make noise on the audio (ie telephone), they also to an extent block the audio devices from interfering with the digital signal as well.
The microfilters which have a connection for the telephone and the router really only filter the audio side, the router side is just connected directly to the phone line, it acts as a convenient splitter, but is generally passive otherwise.
As I mentioned earlier, you can do this at the master socket, so no extensions need any sort of filter, since they are all filtered at the master socket, this also tends to make for a more reliable ADSL connection, since the house wiring has little or no effect on the ADSL. The downside is that the router has to be situated near to the master socket, since it will not work anywhere else.