TDS refers to Total Dissolved Solids; this include all dissolved organic & inorganic substances in the water. However, the TDS reading does not tell us what is in the water. What makes up the TDS value is important.
100pm of Calcium in water (high TDS) is relatively harmless while 5ppm of copper (low TDS) will kill most aquatic life.
What makes up the TDS value matters infinitely more than the value itself.
Very high levels of TDS can induce salt stress in plants/livestock. However, unless you know what the TDS value comprises of (what elements are dissolved in the water to give rise to the TDS value), it is hard to say at what PPM it becomes harmful. Freshwater by definition has less than 1500 ppm TDS, while seawater is generally more than 5000ppm. By no means does this mean that if you have water below 1500ppm it is fine ! The advantage of having a lower TDS reading is that generally it means you have less unknowns in the water column.
However, if one tests tap water regularly, and find that it's TDS value fluctuates a wide range. (more than 50ppm) This is a good indicator that the tap water is unstable, and it would be wise to test the other values as well to make sure they are not too far out of range (KH, pH etc).
Dosing fertilizers in a planted tank will naturally raise the TDS value; in their simple elemental forms most fertilizers are non-toxic to livestock unless over-dosed greatly.
Some sensitive livestock do better in specific ranges. Most commercially available livestock survive in a very wide range - even though elevated salt stress from very high TDS levels may shorten the lifespan of livestock. In controlled tests, White cloud mountain minnows, Corydoras catfish and cherry shrimp survived well in tanks at 1000+ TDS. Natural rivers with very pure water can have TDS values as low as 5 - 20ppm.
TDS is useful as a relative test.
This relative test can also be applied when adding new hardscape or other materials to the tank. If you soak a bunch of stones in a bucket of water, and the TDS rises over time, it means that some part of the rock is dissolving. Totally inert rock will not change the TDS value.
Tanks that use limestone like mine above can see high TDS values at 400+ppm without issues for neocardina shrimp or plants. Other more sensitive species may prefer a more specific (usually lower) range.
This relative test can also be applied to organic waste. Organic waste also raises TDS; unlike what most aquarists think, organic waste doesn't transform magically into just ammonia. Breakdown of organic waste goes through intermediate stages that releases carbohydrates, lipids, proteins, nucleic acids into the water column.
Having a good bacterial cycle quickly decomposes these into simpler elements. High levels of undigested organic waste trigger algae blooms. Organic waste comes from livestock and deteriorating plants (either plants not growing well, or old growth), an easy way to get rid of this is by doing regular water changes.
If you have a matured tank and wonder if organic waste is building up in the water column - whether water changes are necessary; measure the rate of TDS increase over time. Even as ammonia, nitrite/nitrate readings remain at 0, tanks that build up dissolved organic waste over time will see rising TDS values.
Many natural planted biotopes have extremely low TDS ranges; 25ppm and below. Plants are very good at scavenging low levels of nutrients. Plants can still grow well by taking in nutrients from the substrate zone even if the water column is very lean. The important thing is to make sure all nutrients that plants requires are present rather than target a certain TDS range in a particular tank.
Brian Jones's tank here runs well on a TDS of just 30ppm.