The fastest way to find out when somebody birthday is would be to use 2 or 3 seperate INT columns and probably an addition column to store the whole thing as a DATETIME. While you don't normally use ints nor multiple columns to represent date, keep in mind if you have a lot of rows in this table, doing something like
SELECT * FROM people WHERE birthday LIKE '%-12-24';
is not very efficient. It works fine in smaller datasets but because very slow if we start getting into tens of thousands or more (depends on your hardware). Sometimes you need to store data in unusual ways to keep your system efficient, the tiny amount of HD space you waste by having up to 4 sets of date columns (month, day, year, and store the whole thing as a datestamp) pays off in speed.
By doing this you can simply do:
SELECT * FROM people WHERE birth_month=12 AND birth_day=24