Digital Subscriber Line. Broadband - competes mostly with cable modem technology for adoption rate. Comes in many flavors, like ADSL, RADSL, HDSL, and more - which is usually why it's referred to as either DSL or xDSL. Speeds range from 384k all the way up to somewhere around 8mbps and higher, so DSL usually means a fat pipe.
DSL is preferred by a lot of ISPs because of its direct nature, and the fact that they don't have to go through proprietary networks to reach the end user - just POTS.
Main advantage is the use of POTS over other, more expensive or proprietary line types. Secondary advantages include non-variability in speed compared to cable modems.