Belief propagation (BP) is an algorithm (or a family of algorithms) that can be used to perform inference on graphical models (e.g. a Bayesian network). BP can produce exact results on cycle-free graphs (or trees). BP is a message passing algorithm: messages are iteratively passed between nodes of the graph (or tree). The marginal probability of a random variable (or node) is then estimated from these messages.
In the case the graph contains loops (or cycles), the algorithm is called loopy belief propagation and it is not an exact inference algorithm (that is, it doesn't produce exact results).
What is the difference between belief propagation and loopy belief propagation, in terms of operations that they perform in order e.g. to find the marginal probability of a random variable? How do BP and loopy BP differ?