Emery cloth is a type of abrasive

Abrasive

An abrasive is a material, often a mineral, that is used to shape or finish a workpiece through rubbing which leads to part of the workpiece being worn away...

 that has emery

Emery (mineral)

Emery is a very hard rock type used to make abrasive powder. It largely consists of the mineral corundum , mixed with other species such as the iron-bearing spinels hercynite and magnetite, and also rutile...

 glued to a cloth backing. It is commonly used in metalworking by hand. A finer, less commonly seen grade has a paper backing

Emery paper

Emery paper is a type of paper that can be used for sanding down hard and rough surfaces.It can also be used for resistant technology purposes to give a smooth, shiny finish to manufactured products and is often used in the finishing of high-end watch movements.Similar to sandpaper, it is made by...

 instead.

Grades

The grade of the cloth defines the coarseness or fineness of the abrasive. Emery is rated on the average grain size glued to the backing. Common sizes are, from coarse to fine: 40, 46, 54, 60, 70, 80, 90, 100, 120, F, and FF. A 46 or 54 grade cloth is used on roughly filed work, while 60 to 90 grade cloth will give a good polish.