In general, a KEY is a column (or combination of columns) that uniquely identifies each row in the table. It is possible to have multiple KEYs in a table (for example, you might have a Person
table where both the social security number as well as an auto-increasing number are both KEYs).
The database designer chooses one of theses KEYs to be the PRIMARY KEY. Conceptually, it does not matter which KEY is chosen as the PRIMARY KEY. However, since the PRIMARY KEY is usually used to refer to entries in this table from other tables (through FOREIGN KEYs), choosing a good PRIMARY KEY can be relevant w.r.t. (a) performance and (b) maintainability:
(a) Since the primary key will usually be used in JOINs, the index on the primary key (its size, its distribution, ...) is much more relevant to performance than other indexes.
(b) Since the primary key is used as a foreign key in other tables, changing the primary key value is always a hassle, since all the foreign key values in the other tables need to be modified as well.