Start with not discussing computers having a mind. The metaphor that I've usually seen working well with neophytes is variables (or memory locations, depending on context)-as-boxes, and assignment and mutation as putting something in the box or doing something to whatever is in the box, respectively.

"Mind" is a fuzzy concept that lacks the concreteness of boxes, and makes a poor (in utility terms) metaphor for program state (no matter that it might actually be reasonably analogous -- most people don't have a good concrete intuition about the operation of minds to make it a useful metaphor.)

You can even make it physical: http://aturingmachine.com/