A navigational aid, often used for road rallying.
A romer is a square of plastic which may be opaque or transparent. Each romer is designed to work on a specific scale of map (1 inch to 1 mile, 1:50,000 etc), or may have a variety of markings for various scales - there may be a single romer suitable for 1:50,000 and 1:25,000.
They are very easy to lose, so the first thing you should do is punch a hole in the corner, and thread a loop of string through them for hanging round your neck.
The main use is to quickly locate a point from a 6-figure grid reference. The romer is placed on the map with the left and right sides lined up with the grid lines, and the appropriate value on the vertical scale on the horizontal grid line. This places the top of the romer in the correct vertical location. The horizontal position is located by reading the horizontal scale.
A secondary, optional, use is for avoiding no-go and quiet areas. Some romers are marked with circles of specific radii. These correspond to 100 meters, 200 meters for instance. If there is a quiet area around a specific building, the circle can be placed on the map, with the center point on the building in question. Any parts of road which lie within the circle are out of bounds. Rallies tend to use standard no-go areas, which correspond to those on available romers.