What is the moat on a lawn around a stately home called which keeps out animals?

You mean a dry ditch, with a wall on the house side?

It's a ha-ha (!!!)

The idea was to allow animals to graze in the grounds while preventing them getting too close to the house - the illusion of living in a natural landscape.

There are many suggested explanations of the derivation of the name - see for example:

http://en.wikipedia.org/wiki/Ha-ha