TDS is what we use to measure the purity of water. Its the TOTAL amount of DISOLVED stuff (impurities) that you would find in a sample of the water. The lower the TDS the cleaner the water.
TDS applies to freshwater. In saltwater, the amout of "solids" (salt) are too high to be of value. They use other measures such as DOC (dissolved organic compounds) and other metric.
TDS, as mentioned above, is used to gauge the purity of freshwater and performance of water filter. TDS of RO water is usually less than 10 ppm, while RO/DI is usually less than 2 to undetectable.