In probability and statistics, base rate generally refers to the (base) class probabilities unconditioned on featural evidence, frequently also known as prior probabilities. In plainer words, if it were the case that 1% of the public were "medical professionals", and 99% of the public were not "medical professionals", then the base rate of medical professionals is simply 1%.
In the sciences, including medicine, the base rate is critical for comparison. It may at first seem impressive that 1000 people beat their winter cold while using 'Treatment X', until we look at the entire 'Treatment X' population and find that the base rate of success is actually only 1/100 (i.e. 100,000 people tried the treatment, but the other 99,000 people never really beat their winter cold). The treatment's effectiveness is clearer when such base rate information (i.e. "1000 people... out of how many?") is available. Note that controls may likewise offer further information for comparison; maybe the control groups, who were using no treatment at all, had their own base rate success of 5/100. Controls thus indicate that 'Treatment X' actually makes things worse, despite that initial proud claim about 1000 people.
The base rate fallacy
A large number of psychological studies have examined a phenomenon called base-rate neglect or base rate fallacy in which category base rates are not integrated with featural evidence in the normative manner. Mathematician Keith Devlin provides an illustration of the risks of this: He asks us to imagine that there is a type of cancer that afflicts 1% of all people. A doctor then says there is a test for that cancer which is about 80% reliable. He also says that the test provides a positive result for 100% of people who have the cancer, but it also results in a 'false positive' for 20% of people - who actually do not have the cancer. Now, if we test positive, we may be tempted to think it is 80% likely that we have the cancer. Devlin explains that, in fact, our odds are less than 5%. What is missing from the jumble of statistics is the most relevant base rate information. We should ask the doctor "Out of the number of people who test positive at all (this is the base rate group that we care about), how many end up actually having the cancer?". Naturally, in assessing the probability that a given individual is a member of a particular class, we must account for other information besides the base rate. In particular, we must account for featural evidence. For example, when we see a person wearing a white doctor's coat and stethoscope, and prescribing medication, we have evidence which may allow us to conclude that the probability of this particular individual being a "medical professional" is considerably greater than the category base rate of 1%.