The main purpose of moats was to make the central site difficult for enemy soldiers or raiders to access or, in the case of 3-sided moats of the style commonly found in Anglo-Norman manors, to focus attacks in a particular (heavily defended) area. That idea wasn't new in Europe, people had been choosing easily-defendable settlement sites for millenia.

Moats were not necessarily filled with water. Where water wasn't available they could be left as dry ditches with a raised outer banking formed from the spoil. They might be used as a midden (rubbish dump), as a toilet, or filled with additional obstacles.

Moats were only filled with water when there was water available to do it with, normally by diverting or damming a stream or digging a waterway (technically an aquaduct) to a lake. Fish ponds were an important part of settlement sites and it wasn't unknown for wet moats to be used to breed fish for the main house or monastery.

The technology required to build watered moats was easily accessible to builders - humans had been manipulating water sources for hundreds of years. In later periods, roughly from the end of the 14th century, moats became less about defence and more about ornamentation - a demonstration of one's might and importance.

As large-scale landscaping became popular in the era of designers like Capability Brown there was a resurgence in the building or conversion of moated properties, and this time they were almost always filled with water that had been diverted as part of the larger landscaping works.

Sources:

Britain's Medieval Castles, Hull L, 2006

Medieval Ornamental Landscapes, Taylor C, 2000

Moated sites in Medieval England, Coveney N, 2015

Monasteries in the Landscape, Aston M, 2009