They are booking classes.

In general, for most airlines...

F (and sometimes A and P) represent first class.

J (and sometimes C and D) represent business class.

Y (and sometimes B - and maybe others) represents "full coach" (e.g., few restrictions, refundable)

Most other codes are variants of discounted economy.

If you have specific questions about an airline, you can Google it and find either an official or unofficial website that lists the codes and what their rules are. (Usually the "unofficial" sites - some maintained by FT'ers - are the best ones because they tend to address upgradability and mileage accrual.)

You can also search your favorite airline board here: most of the major ones have a thread dedicated to the ranking of fare classes.