Question

Also, when is it appropriate to use one?

Answer 1

An index is used to speed up searching in the database. MySQL has some good documentation on the subject (which is relevant for other SQL servers as well):
http://dev.mysql.com/doc/refman/5.0/en/mysql-indexes.html

An index can be used to efficiently find all rows matching some column in your query and then walk through only that subset of the table to find exact matches. If you don’t have indexes on any column in the WHERE clause, the SQL server has to walk through the whole table and check every row to see if it matches, which may be a slow operation on big tables.

The index can also be a UNIQUE index, which means that you cannot have duplicate values in that column, or a PRIMARY KEY which in some storage engines defines where in the database file the value is stored.

In MySQL you can use EXPLAIN in front of your SELECT statement to see if your query will make use of any index. This is a good start for troubleshooting performance problems. Read more here:
http://dev.mysql.com/doc/refman/5.0/en/explain.html