There are two purposes in eyecatches in cartoons. One, is to show the development of a cartoon,anime or tokukatsu program and two, part of the merchandise. The first purpose is that some characters are showing themselves or with other of their supporting characters in order to identify them. Examples of those eyecatches are from Yu-Gi-Oh! GX which shows the main characters with their main monster cards, and another Shakugan no Shana which also shows different main characters of that show. The second purpose in the other hand, is only support the merchandise of the show by knowing many characters on a eyecatch. Example of that is Pokemon where each eyecatch in all episode show's the "Who's That Pokemon?" where the children guess a Pokemon who's in the silhouette in order to be familiar in the anime's video games. There are also anime or cartoon shows which there are no eyecatches in every episode.Examples are FullMetal Alchemist and the Big O.
Some examples of eyecatches in anime....
An eyecatch from the Japanese version of Pokemon Advanced featuring May,Max,Brock and Ash with the legendary Pokemon at the background.
Another eyecatch from the another anime entitled "Moetan" featuring Ink.