Storing large volumes of a text in a database column without optimization, then searching for small strings within it. It causes the database to basically search character by character to find a match by reading everything from disk. If you use indexes the database can do a lot of really incredible optimization to make finding values mich faster, and honestly string searching is better suited to a non-relational DB engine (which is why search engines don't use relational DBs).

Cartesian explosion is where you join related data together in a way that causes your result set to be wayyyy bigger than you expect. For example if you try to search through blog posts, but then also decide to bring in comments to search, then bring in the authors of those comments and all their comments from other posts. Result sets start to grow exponentially in that way, so maybe if you only search a few thousand blog posts you might be searching through millions of records because you designed your queries poorly.