A foreign key is basically a column on one table that can only contain values from a column on another table.
So, for example behind this forum there may be two tables, USERS and POSTS. The USERS table will have a column (probably the Primary Key) called something like USERID as well as other columns. The POSTS table will also have a USERID column and this will only allow values that exist in USERS.USERID in order to ensure that every post links to a valid user.
Note that a User ID can only exist ONCE in USERS but can exist any number of times in POSTS - because a user can make lots of posts.
In a database, the foreign key column will usually be indexed as it will frequently be used in joins.
