Therapies often work for reasons completely unrelated to the reason they claim to work. In the case of EFT, this looks very similar to eye movement desensitisation and reprocessing (EMDR) which is also regarded by some as a load of bunk, but I know some actual research has been done to determine why it might be helpful. It is often used for anxiety disorders and PTSD.
Simply put, EMDR involves making deliberate eye movements while recalling traumatic events or things that make us anxious. One theory goes that we only have a limited amount of attention we can give to anything at one time. If we do something else which requires attention at the same time as thinking of the traumatic thing, then we have less attention to spare and therefore the emotion experienced is less intense. Gradually the negative emotions are decreased in this way. Finger tapping in EFT would seem to play the same role as eye movements, and this might explain any success there is with emotionally linked problems. Its sort of a way of doing graded desensitisation like they often use in phobias, but in cases where the initial exposure might cause too much distress for the therapy to work.
In addition you have the placebo effect working too, which is considerably enhanced by talking about big overarching theories about energy etc.
Here's a research paper into the theory.