Basically the idea that 'like effects like'. Voodoo is a prime example of sympathetic magic. Abusing a doll as the representative of the person you wish to abuse in the expectation that they are sympathetic with one another. Another is 'Psychic detectives' asking for an object of a missing person in order to 'view' their location. It also forms the basis for most superstitions, such as a lucky charm or ritualistic behaviour. A catholic crossing himself before a lottery, or a football fan wearing lucky socks before a game because when she did that last time they won are examples. There is no actual logical link between these acts and the desired outcome but believers at some level think they are in sympathy with one another and in doing so there is some form of cause and effect.
Sympathetic magic forms the basis for a whole host of modalities and bad ideas but no matter how smart or skeptical we believe ourselves to be, human beings from all walks of life fall prey to it from time to time. Take for instance an interesting test done by psychologist and cognitive neuroscientist Bruce Hood: at several scientific and skeptical conferences he has challenged audience members to put on a garish jumper. It has been cleaned and washed and looks just like any jumper many of us would buy - sartorial choices aside. Almost everyone says: of course they would. But, he then tells them the jumper once belonged to notorious serial murderer Fred West; would they now be prepared to put it on? Hood reports that members of the audience will physically recoil from the few people who say they are willing to wear the jumper. A moment's thought tells us that it is ridiculous, it's a jumper. We can't 'catch' serial murdering from it. But these ideas of sympathetic magic are deeply ingrained in us and often lead us to make poor unscientific choices
Anthropologists posit that this human trait of misunderstanding cause and effect between objects or events forms the basis of religion and of the earliest human art such as cave paintings. It could be seen as the precursor to scientific thinking. Science tries to weed out cause and effects that don't exist so that we can take efficient accurate actions that really do have an affect on our environment. But we are still human and no one is immune, nor sometimes would many of us want to be. How many of us hold onto objects that have a purely sentimental value to us - a christmas tree bauble we bought on a that memorable trip to Prague (that we could have bought anywhere), a chipped bowl that our grandfather used every day or a necklace from a lover. Any of these could be swapped for something identical but we'd believe the link was broken if they were. But however magical it may seem, that has more to do with biology and psychology than with metaphysics.