The term "Broadband" refers to Internet connectivity that is faster than dial-up. There are many forms of Broadband; ADSL, Cable, ISDN and Satellite are common household forms.
Generally, Broadband is "always on"; there is no dialling, no engaged signal or extra costs associated with each time you connect. You can generally make and receive phone calls while you're on the 'net, so you won't need two phone lines.
If you want ADSL Internet, your local telephone exchange must be enabled for ADSL, but you may not be able to take advantage of it. A few limitations exist, the main one is a distance of up to 4km from the exchange (as the wire runs, not as the crow flies).
ISDN is available only in limited locations but for the rest of us, not all is lost. There is Government HiBIS funding available for those who cannot use ADSL.
Satellite connectivity can be expensive to purchase and costly to run. HiBIS pays for hardware and installation and subsidises the monthly usage charge.
HiBIS funding is sorted out by your chosen provider, rather than requiring you to apply in triplicate.
Broadband is a useful tool and it may help you.