If you were to graphically represent a "typical" lineage you get a tree with simple branches. When there is reticulate evolution, branches of the tree fuse together to form a net-like graph. In reticulation, recombination of genes from different lineages is the driving evolutionary force (ie. hybridization, backcrossing, polyploidy, etc.).
It's hard to tell how much of a role reticulation plays in coral evolution because the phylogeny (which is reflected by the taxonomy) is a huge mess. We can't even figure out what a species is. We know that some corals "hybridize" and at least in the lab many produce fertile offspring. However, if they're just members of one large polymorphic species then they're really not hybrids and there is no reticulation. Even if they are truly separate species we don't know how much that hybridization occurs in the wild.
Probably the best studied case of reticulation in coral evolution is the Caribbean Acropora and people are still arguing over the evolutionary role of reticulation there. A. prolifera is a hybrid of A. palmata and A. cervicornis, but it's infertile. Still, it reproduces asexually, so some argue that it's a valid species since there are plenty of other animals with no sexual reproduction. Some people also think there is evidence that it can backcross with either of the parent species, which ties the two of them together even if it isn't a true species. Still others think there is no more evolutionary significance to it than any other infertile hybrid, so it doesn't represent a fusion of lineages.