An alternate key (the correct term, though "alternative key" would be better English) is a column or set of columns other than the primary key that is also a unique key for the table. Some tables will have them, some will not. If you recognise that your table has alternate keys you should usually create UNIQUE constraints on them.
An example (off the top of my head): a hotel room reservation table may have a primary key "reservation_number". However, since no room can be reserved twice on the same day there are also alternate keys of (room_number, from_date) and (room_number,end_date).
OK I think Andrew's reply is complete (as always) but just my 2 cents to clarify a bit more
There is a concept in RDM named by "Candidate Key" that by definition is a unique key. What does it mean?
It means you can uniquely specify each tuple (a.k.a row, record...) by that but it is not just unique! It should be minimalist too: If you could specify each tuple using a 2 column key and also a 3 column key, the 3 column one is not a Candidate key (BTW,They called this super key: do not panic!).
After you determine the candidate key collection (yes they may be more than one CK but all should have the same number of columns), you choose one of them as your Primary key and other remaining CKs would be called Alternative keys.
There is no obvious usage for Alternate keys in my opinion because you have (and should have) a chosen PK so the remaining CKs are just good in designing phase of database. Note that RDM is silent about choosing PK but you should compare the potential CKs from some practical view of point such as performance.