"In the 1800s, starting around the time of the Civil War, thrifty homemakers would use scraps of wool or felted wool from old clothing, blankets and hats to create designs for mats or rugs. Using coins as templates, they created circles and each piece was then stitched in blanket stitch fashion. (Thus, the name "penny" rug). Sometimes, the mats or rugs were backed with old burlap bags or feed sacks. Sometimes a penny was stitched inside the mat to make it lie flat.
Penny rugs are not actual rugs for the floor, but decorative coverings for beds, tables and dressers and mantles. Sometimes they are used as wall hangings or pillows. Most designs include circles and some include images from everyday life such as cats, flowers, birds and shapes such as stars and hearts.
Penny rugs are made by selecting good quality 100% wool. It must not be too thick. It may be hand-dyed or overdyed to give the piece dimension. Circles are cut from the wool in varying sizes and then stitched together concentrically using complementary colors. The circles are stitched to a wool backing in a pleasing design. When finished the entire piece should have a backing to cover the stitches and to protect it. The backing may be wool, linen or burlap."
from wikipedia
http://www.astorybooklife.com/how-to/penny-rugs/
"Although circles were the main shape used in early designs, any shape imaginable could be used in current designs. I have seen some beautiful pieces made with shapes such as; stars, hearts, snowman, crow, and trees. There’s really no limit to the designs that you could come up with, you simply want to be sure that the pattern can easily be hand stitched around each edge."