A Zapper is a small electrical gadget, usually battery powered. Sizes range from a lump about the size of a short stack of quarters to almost as big as a paperback book. There are two contacts which you hold in your hands, and the device makes a small electric current pass through your body from one contact to the other. The electric current is a low to medium frequency square wave (specific parameters vary among manufacturers). Some people report feeling a slight tingle, others feel nothing. The standard session is 61 minutes: hold the contacts for 7 minutes, release for 20 minutes, hold for 7, release for 20, hold for 7.
Although a couple of manufacturers have made public offers (such as Parazapper, a frequent contributor to this forum), there has been no clinical study that I've been able to find which determines the effectiveness of a Zapper. I'm sure I'll get a lot of grief for that statement, but it's true anyway. Clark reports results in her books, but there are no details of her trials (number of subjects, screening, control groups, test parameters, variables. etc.)
The idea is that a small, unipolar electric current with high frequency content will kill parasites and harmful bacteria which cause and sustain disease. There is plenty of evidence, outside the Zapper community, that a small electric current will kill small things. There is no explanation of how the electricity kills only the bad guys, but leaves the good guys.
While there is a lot of focus around here on the Zapper device itself (which is the "best" frequency, best voltage, best contact material, etc.), the Clark books stress a more complete approach to health improvement, including diet changes, removing harmful substances from your environment, and removing toxins from the body with different "cleanses".