Scientific research on biological problems works best when researchers can observe two groups of essentially identical individuals who are living in an essentially identical situation and are treated in the same way except for one factor. One group (the "test group") is given an experimental treatment—a new medication, say—and the other group (the "control group") is not. In other words, we hold everything constant except for a single variable (or sometimes a small number of variables) that's different for the two groups, and then we see how the difference plays out.
Mice can be easily divided into two groups—one group in one cage, the second in another—and treated identically except in the one respect that a researcher is studying. Some statistical tricks allow us to simultaneously juggle a few variables in an experiment and (with some degree of accuracy) to separate out the various effects caused by each manipulation. This kind of control isn't usually possible in human experiments. We normally can't assign people to groups before an experiment starts or direct exactly how they are to live their lives, holding everything constant save the particular factors we are interested in. Usually, the best we can do is to look through the wrong end of a telescope at very large groups of people as they go about whatever they happen to be doing, making cautious, plausible guesses about which of the differing effects of treatment that we observe between the test and control groups are pertinent and which aren't, which associations are causal and which are accidental. We may imagine that the value of a study comes from the power of its statistics, but what matters most is much more subjective: the validity of our assumptions.
In addition, research using human subjects is often confounded by unconscious (or, rarely, conscious) prejudice and expectations on the part of experimenters and participants. Just wanting a certain result can affect the outcome of an experiment: A patient might report feeling better if he or she thought that a treatment were effective, and an experimenter might interpret results differently as a result of an unconscious attraction to a certain outcome. For that reason, the best method is to assign subjects randomly to an experimental or control group. This minimizes the effects of differences in the makeup of the groups. "Double-blind" studies, in which neither the experimenter nor the subject knows who has been given an active treatment or a placebo, add to the strength of research by minimizing psychological effects that might alter the outcome.