In 1987, the FCC floated a proposal to have computer bulletin board operators pay an extra charge for their phone service. The FCC withdrew the proposal in 1988, but some people never got the word. There's a new story going around that sounds awfully similar to the modem tax, but it's real. Before going further, let's review Modem 101, to help see why this issue comes up at all.
Modems are devices that let computers send data over phone lines.
On the other end, another modem turns those noises back into information. In the course of a typical connection the modem will have lots of idle time, but the phone network has no way of knowing or taking advantage of this. As far as it's concerned, the modem connection is just one long screech, and the line is tied up for its duration. Since an ISP is essentially many POTS lines connected to many modems connected to controller hardware connected to the Internet, ISPs buy lots of business phone lines from the phone companies. Nevertheless, the phone companies aren't happy.