Flash cards work for two main reasons:
- they serve as retrieval practice
- they force the student to space practice out
Both of these reasons have been demonstrated to enhance learning.
Retrieval practice, sometimes called the testing effect, has been shown by Roediger and colleagues to promote learning above and beyond additional study. For instance, in a 2006 study by Roediger and Karpicke, some subjects studied material several times then took a test (SSST, where S = study and T = test), whereas other subjects studied material less then took a several tests (STTT). After a brief delay, memory was shown to be better for those who had self-tested relative to those who hadn't. In a 2007 study by Karpicke and Roediger that actually used flash cards, the memorial benefit was always greater when individuals self-tested rather than merely restudied -- and importantly, best when individuals continued to self-test even when they thought they had the information down cold. This suggests that you shouldn't "drop out" flash cards from the deck if you get them right once or twice. Another 2006 Roediger and Karpicke paper provides additional evidence in more applied contexts.
The spacing effect is also a powerful influence, here, as well. Research by Bjork and colleagues on a parsimonious (yet slightly circular) idea called desirable difficulties provides one theoretical example for why this is so. Learning is most powerful when it is most difficult, and spacing out your study (or, as above, your test) provides that information with time to decay (or be interfered with by other memories) such that when retrieval is successful, it is rather potent. Note that one concern with spacing is that if study is pushed too far out, successful retrieval cannot occur, leading to no benefit to memory.