A high SNR simply means how loud the signal is over background noise. The higher the SNR margin the more stable the connection. You have a strong signal and have plenty of head room to receive faster speeds. Generally you would have a high SNR if your on a restricted speed plan eg. 256/64, 512/128 or 1500/256. The faster your connection speed the lower your SNR will be. Generally on unrestricted speed plans like Adsl2+ up to 24mbit the isp will set the SNR margin at which your modem connects generally a range between 6dB to 14dB. This will give you the fastest speed while maintaining a relatively stable connection. iiNet currently allow Adsl2+ customers to choose their own profile which ranges from fastest possible speed (low SNR) to slower speeds (higher SNR).
Attenuation on the other hand is a measurement of the resistance to the signal on the line and should never change regardless of speed.
There are many factors which affect both SNR and attenuation. A few are line distance, gauge or thickness of line, quality or age of line, number of bridge taps on line etc.