What is a mileage charge?

A "mileage charge" is a per-distance charge based on the length of whatever it is you're talking about.

Examples:

Renting a car - some rental companies charge you (indirectly) for the wear-and-tear on the vehicle by charging a per-mile-driven fee.

Leased vehicles often have something like this in their lease - often called an "excess mileage charge" - if you drive more than (for example) 12,000 miles a year, you get ding'd for the excess mileage.

When shipping - trucking companies sometimes add a "mileage charge" to their basic tarrif for delivery to a location that they don't normally go to or if the place is especially obscure or difficult to get to. (like up a mountain on a steep, narrow road.)

Furniture and appliance stores often do this - they have a set delivery fee for any address within a particular radius of the store (or warehouse) - say five or ten miles - and then there is a per-distance charge for places outside of that central area.

Other things come with a mileage charge:

If you live in that house, way up on the top of that mountain, your local cable company - and the telephone company, may impose a "mileage charge" for stringing the wires out in the middle of nowhere.