There's a list of things. Actually, with increased testing, case counts might very well go up even if things are under control, so one big test is a high number of negative tests, which indicates a state isn't chasing sick people and trying to figure out why, but actually monitoring the population and able to identify outbreaks early. Monitoring versus testing sick people will result in high negatives. Tennessee is doing a good job with testing and about 95% or more are negative each day.
A good example is my mother in law's assisted living place. One of the residents went to ER, and was treated and discharged back. She had no symptoms but was tested at re-entry as a precaution, it was positive (probably a false positive) but then they tested every resident and every staff and every other person going to the center on a regular basis (some outside nurses are allowed in). So that was 200 or so tests and none of them were showing symptoms, all negative. That's what is needed.
Other big signs, from what I've read, are hospitalizations and ICU needs, and deaths obviously.
