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.

If there's something you want to search by in a database, you should index it.

Indexing will create an ordered data structure that will allow much faster queries. If you were looking for the username gazter in an unindexed column, it would have to check literally every username entry. In a table of 1000000 entries it would check 1000000 times.

In an indexed column it might do something like ask to be pointed to every name beginning with "g", then of those ask to be pointed to every name with the second letter "a" and so on. It would find out where in the database gazter is by checking only six times.

Substring matching is much more computationally difficult as it has to pull out each potentially matching value and run it through a function that checks if gazter exists somewhere in that value. Basically if you find yourself doing it you need to come up with a better plan.

Cartesian explosion would be when your query ends up doing a shit load of redundant work. Like if the query to load this thread were to look up all the posters here, get all their posts, get the threads from those posts and filter on the thread id.