A Tack Cloth removes loose dirt, hairs and so on from surfaces about to be painted with oil based paints.
They may be bought very cheaply from builders merchants, or are easy to make using a mixture of a little linseed oil, a few drops of turps & glycerine. The mix is stored in an airtight jar, and applied to damp lint free scrim to make a tack cloth.
Other Paint Types
Note this is only for use with oil-based paints. Using water-based paints (acrylic etc) a wipe down with a cloth dampened in clean water should suffice, and oil from a tack cloth may prevent the paint from adhering properly. For other sorts of paint such as cellulose the oils on a tack cloth may interfere with adhesion of the paint. Surfaces can possibly be wiped with a cloth dampened with the appropriate paint thinners.
Tack rags only problems if cloths have been over-oiled. Use of suitable amounts of oil results in at most trace amounts of residue on paintable surfaces, and linseed oil is compatible with and sometimes included in water based paints.
Linseed oil tack rags are vulnerable to spontaneous combustion, so rags made with linseed should be stored in a fire safe container.