DSL = "Digital Subscriber Line" - high-speed access to the Internet through the same two wires your phone service comes into your home on. As its name implies, the data is not transmitted by analog means (voltages or frequencies fluctuating in lock step with your voice), but digitally (with zeros and ones, or a binary number which represents, for example, a measurement of those voltages or frequencies). Because of this, DSL doesn't interfere with your regular analog phone service. You can therefore have one phone line for both voice calls and high speed access to the Internet.
Unlike with a cable modem, your access speed doesn't get worse as more people log onto the system, because the signal is sent directly to you through your two phone wires and is not on a shared loop of cable subscribers in your neighborhood. One disadvantage of DSL, however, is that you have to be fairly close to a telephone "switching station" (where the phone company keeps its switches that switch a phone call meant for you to your line and only your line (usually).) If you are out in the boonies, you are probably out of luck as far as DSL access goes.