basically any sort of noise that should not be there such as hissing, crackling etc, the line should be totally silent, if there are noises such as crackling that points toward a fault on the line that would need an engineer out to fix, there is a quiet line test, i think you dial 17070, ive never done it so if i am wrong im sure someone who knows more than me will correct me
soapy is part right. Audible noise is easy to identify and indicates a problem with the line; and is likely to be associated with high frequency noise. What actually matters for broadband is the high frequency noise; which you can't hear. It is very difficult (impossible?) to detect without special equipment. You may be able to guess that it is there either from audible noise, or from the behaviour of your broadband.
You will have difficulty deducing much from the behaviour of your broadband unless you use an unlocked modem.