Let's insert a few records in the newly created table books with PRIMARY KEY id.
Notice that while the first two inserts happen successfully, the third insert fails with UNIQUE constraint violated error. That's because, we are trying to insert a record which has a non-unique value in the column marked PRIMARY KEY (inserting 1 as id, after it has already been recorded). This also explains the fact that internally, the PRIMARY KEY constraint on a column employs the UNIQUE constraint too among other things, and we need not specify UNIQUE in case we have already declared a column as PRIMARY KEY.
Go ahead, change the id of the third row to be inserted as anything other than 1 or 2, in the statement above, and Note the result.
Another key thing to notice about PRIMARY KEY constraint is, it can only be declared on one column in a table, unlike other constraints that can be declared on any number of columns. Note the results of the CREATE TABLE statement below that declares multiple columns as PRIMARY KEY.
This also explains the fact why PRIMARY KEY is a table constraint and not a column constraint. There can only be one PRIMARY KEY marked for a table, and that acts as a property/constraint of the table, and not the column itself.