A lot of applications have a requirement to search the full-text of some content they have for some words it might contain. This kind of functionality is often referred to as full-text search. For example, a blogging software might need to provide a search functionality that searches the blog posts for the user entered query terms.
It is not possible to use the regular database indexes (usually B-Trees or Hashmaps) for this purpose because they require that you provide the full value of the column you are searching in; in essence they do an equality search. In the blogging software example, the user would then have to type in the entire blog post verbatim in order to find it; even if you could imagine the most patient of users, if s/he already knows the entire post by-heart, why would s/he be looking for it anyway?!