Thread count is the number of threads per square inch of woven fabric. The higher the thread count, the tighter the weave, giving a softer feel to the fabric.
The general wisdom is that a thread count of higher than 100 is desirable --these fabrics are known as percale -- with somewhere above 180 being ideal. While fabrics are available with thread counts up to 1000, anything in excess of 400 is considered by most to be simply extraneous.
Three additional components are important when considering thread count: yarn size and ply.
Yarn size refers to the thickness of the yarns that are used to make the fabric. A higher yarn size means a finer yarn. Generally sheets are made from a yarn size range of 40 to 100. Obviously, the finer the yarn, the more of them will fit in a square inch.
Ply refers to the number of individual yarns used as a strand. Single ply fabric is woven from one, individual yarn; 2-ply fabric is made from yarns that are twisted together and then woven. If 2-ply yarn is used, the finished construction will have twice the thread count of the same construction made from single ply yarn. 2-ply yarn must be made from a very high yarn size (like 100) or they will feel thick and heavy.
Another important consideration is fiber. Sheets may be made from various cottons, various cotton blends, polyester, or other man-made fibers. Cotton/polyester blends outsell cotton sheets largely because they wrinkle less and cost less. Be sure the read the label to determine the amount of cotton in the sheets. It may say Egyptian or Pima cotton (high quality, soft, strong types of cotton), but contain only a small percentage of it.