In databases indices are usually used to enhance performance when looking for something defined in your where clause. However when it comes to filtering some text, e.g. using something like WHERE TextColumn LIKE '%searchstring%' then searches are slow, because the way regular database indices work are optimized for matches against the ‘whole content’ of a column and not just a part of it. In specific the LIKE search which includes wildcards can not make use of any kind of index.
As mentioned in the comment below MySQL needs the MATCH () ... AGAINST syntax to search within a fulltext index; BTW this varies depending on the database vendor. In MS SQL you can use CONTAINS so keep this in mind when you plan to support other databases too.
Fulltext indices work better for regular text, because they are optimized for these type of columns. Very simplified: They split the text into words and make an index over the words and not the whole text. This works a lot faster for text searches when looking for specific words.