Health of a stream is measured by a number of parameters (which can be further classified into primary, secondary and tertiary) including temperature, pH, turbidity, color, odor, dissolved metals, dissolved oxygen, solids, bacteria, nutrients, etc. Scientists take samples from streams and also take photographs of the area to assess the health of the stream. The samples are tested for various water quality parameters in the laboratories.
In my opinions, temperature, pH and color would be the three crucial parameters for health of a stream. Temperature affects not only the rates of reactions, but also the healthy survival and growth of phytoplanktons and zooplanktons. Many of the reactions taking place in the stream are a function of its pH. Extreme pH can be deadly to organisms. Color is, generally, an indicator of presence of organic impurities (or their decomposition) in the water (except for the case when dyes may have been discharged into stream). Organic contamination will consume dissolved oxygen, thereby decreasing the quantity of oxygen available for fishes and plants.
There can be a number of other parameters for defining the health of stream and their relative importance will vary from case by case.
Hope this helps.