Cowrie" is about as descriptive as "fish" and we can't tell anyone much from that. Depending on who you ask, "Cowrie" is the common name for any snail that has a shell which is sort of folded around itself, and has a mantle which extends to cover it's shell (or part of it) when the animal is active (this would include both the Cypraeids and the Ovulids) or specifically those snails of the genus Cypraea. In either case, despite the claims of your local pet shop, most species are predatory (feed on animal prey) rather than herbivorous (feed on algae). There are literally hundreds of species of Cypraea, and their diet range is just as wide as the number of species -- ranging from general scavengers to generalized omnivores to highly specific predators. Many different species are commonly imported for the reef trade, and most look so similar that it takes an expert to be able to specifically identify them. It is common to see gastropods are misidentified in pet shops, and unfortunately for you as a consumer, it is almost impossible to tell what the diet will be from any common name (the suppliers give the animals simple common names, and unless the pet shop staff really knows what the snails look like, they have nothing else to go on). I often see several different species in a tank with a single name on them, and all of this is working against you when you're trying to figure out what you have and how to care for the animal.
Despite that problem, if you can identify the animal there are a number of generalizations that you can safely make about the different groups. The egg & spindle cowries (Ovulids) are primarily cnidarian predators, typically specializing on one or a few species of soft corals, although many species may accept other foods (even algae) if they get hungry enough in an aquarium. For example, the Flamingo Tongue (Cyphoma gibbosum) may be one of the most commonly photographed snails in the Caribbean, and preys exclusively on the tissue of gorgonians. Likewise the "true" cowries (genus Cypraea) are frequently specialists on colonial invertebrates, such as tunicates, hydroids and especially sponges – if you count the number of cowries that consume a given prey item, sponges are certainly the winner. Although I say that these animals prefer a certain prey item, they should probably be considered omnivorous, really.