Cleopatra's pool at Siwa has nothing to do with the very well known Queen Cleopatra VII! the name makes it sound like an historical place, but there is no reason to believe that Cleopatra had anything to do with it.
However, it indicates that the place is one of Siwa's nicest pools. Nowadays it is used by local men as well as tourist groups for bathing. It was formerly used by local brides for bathing, but that practice has now moved to the nearby Tamusi bath, which is more secluded. There is a little nice coffee house by the pool sheltered from the sun and good for hot days.
If you are to book an excursion at Siwa that includes Cleopatra's pool, make sure you prepare your swimming costume for a little nice experince with the natural water of the pool.