use the measure tool if you wanna make it manually or if you wanna do it automatically, you could:
- extract your countour lines in two distinct shapefiles (selecting them within the table of attribute of your shapefile, then right click on the shapefile and extract data, selected features)
- then creating points along one contour line (edit tool in the editor toolbar, click your line, click editor menu, click construct points, set number of points and distance)
- and finally use the Near (analysis) to to calculate the metric distances between the points in your first contour line to the closest edge of the second contour line.
You get a table with the point distances to the second contour line, that you can average and analyse.
There might be easier ways, this is the first that came up im my mind.