Although what is monitored and the exact name may be different depending on manufacturer, the overall information is pretty much the same. Below are some of the common terms and measurements used to judge line quality. Remember these are not hard numbers but simply a generalization of line statistics:

SN Margin (AKA Signal to Noise Margin or Signal to Noise Ratio)
Relative strength of the DSL signal to Noise ratio. 6dB is generally the lowest dB manufactures specify in order for the modem to be able to synch. In some instances interleaving can help raise the noise margin to an acceptable level. Generally speaking, as overall bandwidth increases, your signal to noise ratio decreases. So a customer that upgrades from 1.5 to 6.0 service will typically see a corresponding decrease in the signal to noise ratio. The higher the number the better for this measurement.
6dB or below is bad and will experience no synch or intermittent synch problems
7dB-10dB is fair but does not leave much room for variances in conditions
11dB-20dB is good with no synch problems
20dB-28dB is excellent
29dB or above is outstanding

Line Attenuation
Measure of how much the signal has degraded between the DSLAM and the modem. Maximum signal loss recommendation is usually about 60dB. One of the biggest factors affecting line attenuation is distance from the DSLAM. Generally speaking, bigger distances mean higher attenuation. The lower the dB the better for this measurement.
20dB and below is outstanding
20dB-30dB is excellent
30dB-40dB is very good
40dB-50dB is good
50dB-60dB is poor and may experience connectivity issues
60dB or above is bad and will experience connectivity issues