One way to explain it-

Find a bolt on something and a wrench that fits it. Have her hold the wrench close to the head and have her try to loosen the bolt. Then have her hold it further out to see how much easier it is to loosen the bolt. Point out on the gears how they are different diameters so you're effectively moving your position on the wrench handle.

Another better approach:
Take a dowel, attach a string to it and a weight on the other end of the string. Have her lift the weight by rotating the dowel. Now put some sort of a spool on the dowel to increase the diameter and have her lift the weight again. Notice how much harder it is to lift the weight? But then she can lift the weight with fewer rotations. Point out that it takes more force to go up hill (bigger weight on the end) so she needs to use the smaller diameter dowel to lift the weight.

You might be able to do this with the bike on a trainer or stand with her turning the cranks by hand as well.

OTOH, I like the approach of having a experienced cycling girlfriend explain it all to her

-murray