When I speak of database relationships, I specifically mean how the data in one table relates to the data in another. A relationship between two tables can be one-to-one, one-to-many, or many-to-many.
The relationship is one-to-one if one and only one item in Table A applies to one and only one item in Table B (e.g., each U.S. citizen has only one Social Security number, and each Social Security number applies to only one U.S. citizen; no citizen can have two Social Security numbers, and no Social Security number can refer to two citizens).
A relationship is one-to-many if one item in Table A can apply to multiple items in Table B. The terms female and male will apply to many people, but each person can be only one or the other. A one-to-many relationship is the most common one between tables in databases.
Finally, a relationship is many-to-many if multiple items in Table A can apply to multiple items in Table B. For example, a record album can contain songs by multiple artists and artists can make multiple albums. You should try to avoid many-to-many relationships in your design because they lead to data redundancy and integrity problems.
Relationships and keys work together in that a key in one table will normally relate to a field in another, as I mentioned earlier. Once you grasp the basics of unique identifiers and relationships, you can begin to normalize your database.