Doilies are small mats, usually circular, that are placed on furniture to protect the finish from large heavy vases and bowls. Doilies are associated with Victorian decor, and were practical as well as ornamental. Furniture of the period was typically dark wood, and polished to a high gloss. An epergne - a large, often metal, vessel meant to hold an arrangement of fruit or flowers - placed in the center of the dining table or on a sideboard, could seriously scratch the surface of one's fine mahogany. Doilies were the solution.
Doilies are most often crocheted out of fine cotton thread, in a round pattern with a lot of openwork, or filet. They can also be knitted, or a plain fabric center can be edged in several inches of crocheted lace border. Doilies should extend at least several inches from beneath the item set upon them - a vase with only a hint of a doily underneath it would appear ridiculous, so get a larger doily for that particular vase.
An antimacassar is a decorative fabric, often in the same pattern of the room's doilies, that is placed over the back or arms of chairs. Macassar oil was a popular grooming product used by gentlemen of the Victorian period to keep their hair in place - thus, the "antimacassar" was to keep the hair oil from the chair fabric. The antimacassar, of course, could be laundered or replaced altogether.
A table runner has a similar function as doilies, to prevent damage to a sideboard or credenza. Table runners can be crocheted filet, but are often woven fabric that has been embellished with embroidery. They are usually made to the size of the table they are to adorn - narrower than the table width, and often much longer than the table length, to drape attractively down either side.
Doilies and their cousins, antimacassars and table runners, fell out of favor in the twentieth century, as large decorative table pieces began to be manufactured with felt on the base to protect furniture, and as the tastes moved away from dark wood furniture. Doilies on a blond wooden table don't present the same as on a darker surface.
Today, if you want to make a period statement, you can recreate a Victorian ambiance with knickknacks under glass bell jars, corner bric-a-brac shelves and the copious use of doilies and other crocheted accent pieces.