Refers to any sample of fabric or carpet borrowed ‘on approval’. The assumption is that the sample is large enough to be of value, so that if not returned it is charged to you, or may be charged up front and credited on return. The purpose of an appro. sample is to allow you to decide its suitability for curtaining or upholstery. It needs to be large enough* for you to understand it: showing the whole pattern repeat, how it looks, drapes and feels en masse, how it reflects light and how the colour changes from daylight to artificial light.
* often 70 x 70 cm – i.e. a half width. Insist on a piece that is at least as long as the pattern repeat. Or, to save the returns hassle, buy one metre and then whether or not you select it for the project you had in mind, you can use it to make cushions or something else.