TDS stands for Total Dissolved Solids, pretty much as it says how much dissolved solids are in your water, (I don't know exactly which solids it does test for though)
Usually most people use a TDS meter to get a reading, it can be in units like g/ml or microseimens.
Ok found a better explanation:
'The principal methods of measuring total dissolved solids are digital TDS meters and testers. These TDS testers (and meters) utilize an electrical conductivity reading through a detachable probe and they are considered the most effective and easy to use.
A TDS meter or TDS tester utilizes Electrical conductivity of water that is directly related to the concentration of dissolved ionized solids in the water. Ions from the dissolved solids in water create the ability for that water to conduct an electrical current which can be measured using conventional Milwaukee meters or testers. When correlated with laboratory TDS measurements, electrical conductivity provides an approximate value for the TDS concentration and is displayed as such on the TDS meter or TDS tester display as parts per million ( ppm ) concentrations and most Milwaukee testers and meters are usually to within +/- 2% accuracy.'
From http://www.milwaukeetesters.com/milwaukee-meters.html