Asymmetric Digital Subscriber Line (ADSL) broadband is a connection provided over home/business telephone lines.
BT owns the UK's landline infrastructure, so when you have an ADSL connection you need to rent your phone line from BT. If you already have an existing phone line, then broadband can be added onto the package.
ADSL broadband's popularity stems from its availability. ADSL2+ connections have become increasingly common, using the same telephone wiring but different software and protocols to provide speeds of up to x faster than ADSL.