As Webster notes below, a swatch is a small piece of material; Swatches are useful when you are planning on buying a large or expensive item and wish to be sure how the color, texture or whatever will go with everything else you have.
Swatches for home furnishings (Couches, armchair, etc) are probaby most common, as well as draperies. Swatches of carpet and other flooring can also be obtained, and even swatches for more expensive clothing to make sure it matches your wardobe. This way you can do comparisons of colours and patterns to see what will match your particular idiom.
They are generally given out freely to those who ask, and by freely I mean free of charge. Any decent Home Furnishings store will be glad to give you one because it will give you a chance to be certain of an item and thus increase the chances of your buying said item.
You can even get color swatches from catalogue retailers like JC Penny, either through their telephone center or through the internet ordersing site; Though the swatches are free, shipping will usually be charged (but is usually only a few dollars for shipping as many swatches as you like).