This is an analogy problem where we need to find the relationship between the two pairs of words.
Step 1: Analyze the first pair (Odometer and mileage).
An odometer is a device used to measure the distance traveled or the mileage of a vehicle. Therefore, the relationship between an odometer and mileage is that the odometer measures the mileage of the vehicle.
Step 2: Analyze the second pair (Compass and ?).
A compass is a device used to measure direction. It helps determine the direction one is facing, similar to how the odometer helps determine the mileage of a vehicle.
Thus, the relationship between a compass and direction is similar to the relationship between an odometer and mileage.
Therefore, the correct answer is:
\[
\boxed{\text{Direction}}.
\]