The PARTITION BY clause sets the range of records that will be used for each “GROUP” within the OVER clause.
In your example SQL, DEPT_COUNT will return the number of employees within that department for every employee record. (It is as if you’re de-nomalising the emp table; you still return every record in the emp table.)
emp_no dept_no DEPT_COUNT 1 10 3 2 10 3 3 10 3 <- three because there are three "dept_no = 10" records 4 20 2 5 20 2 <- two because there are two "dept_no = 20" records
If there was another column (e.g., state) then you could count how many departments in that State.
It is like getting the results of a GROUP BY (SUM, AVG, etc.) without the aggregating the result set (i.e. removing matching records).
It is useful when you use the LAST OVER or MIN OVER functions to get, for example, the lowest and highest salary in the department and then use that in a calculation against this records salary without a sub select, which is much faster.
Read the linked AskTom article for further details.