The primary key is a column in a table.
The primary key needs a unique value, which needs to come from somewhere.
The sequence is a feature by some database products which just creates unique values. It just increments a value and returns it. The special thing about it is: there is no transaction isolation, so several transactions can not get the same value, the incrementation is also not rolled back. Without a database sequence it is very hard to generate unique incrementing numbers.
Other database products support columns that are automatically initialized with a incrementing number.
There are other means to create unique values for the primary keys, for instance Guids.