Signal-to-noise ratio (often abbreviated SNR or S/N) is an electrical engineering measurement defined as the ratio of a signal power to the noise power corrupting the signal.
In less technical terms, signal-to-noise ratio compares the level of a desired signal (such as music) to the level of background noise. The higher the ratio, the less obtrusive the background noise is. The concept can also be understood as normalizing the noise level to 1 (0 dB) and measuring how far the signal 'stands out'. In some instances interleaving can help raise the noise margin to an acceptable level.
In general, higher signal to noise is better; the signal is 'cleaner'.
Attenuation is the gradual loss in intensity of any kind of flux through a medium(i.e. the reduction in signal strength due to length of your phone line). For instance, sunlight is attenuated by dark glasses, and X-rays are attenuated by lead.In ADSL the signal is attenuated by length of copper lines. Attenuation is normally directly linked to the length of your line. Copper is traditionally used in the local loop and the higher gauge of copper will give the best signal, however some lines may have some aluminium or aluminium joints on the line which will increase resistance... as will oxidization of joints. Attenuation is mesured in db or noise. The more noise the weaker the data signal
In general, lower Attenuation is better; the signal is 'stronger'.