If any table have more than one candidate key, then after choosing primary key from those candidate key, rest of candidate keys are known as alternate key of table. 
Or we can say if we have more than one columns that uniquely identify the record in table. And we made one column is primary key then second column will be alternate key.

Here, we will take a simple example of alternate key.
Suppose, we have a table name is Student which has two columns that uniquely identify the records one is St_ID and Another is Email. Now we set primary key in column St_IDthen Email will become Alternate Key. 

Here, we are looking that both columns Sdt_ID and Email are unique in table Student.