What is this lump on the outer part of my ankle that moves?

Varies: There are a number of possibilities. Among the more common can be a ganglion cyst, or a benign tumor such as a lipoma among other potential causes. I would not hesitate to be seen for an accurate diagnosis.

Depends: Could be a fat tumor or ganglion cyst. If it is painful, see a local podiatrist or orthopedist

The lump that moves.: I don't know, I can't see it. The fact that is moves is a good sign. Size, firmness, color or lack of it and pain are all bits of information needed to properly assess the mass. Have a surgeon take a look and then, possibly, you can decide what you need to do.