A bond's par value is what the bond "says" it's worth. The market price is what you actually pay for it. Sometimes they're the same, but in most cases they're not because market prices fluctuate. Those fluctuations ensure that bondholders receive a return competitive with that offered by other investments.
Every bond has a par value, also called its face value. That's how much money the bond issuer pays to the bond holder when the bond matures. If you're holding a $1,000 bond from XYZ Corp. that matures five years from today, then in five years you'll get a check from XYZ for $1,000. It doesn't matter how much you paid for the bond. Whatever the par value is, that's what you get.
A bond's market price is how much you would have to pay to buy that bond on the open market. A newcomer to the bond market might think that a $1,000 bond would sell for $1,000 -- and in some instances it does. But bonds usually sell for something other than par value. That's because a bond's price rises and falls along with interest rates.
Bondholders typically receive interest payments. That's their reward for lending the bond issuer their money. The amount of those payments is determined by the bond's "coupon" interest rate, also called the stated rate. A $1,000 bond with a coupon rate of 5 percent pays annual interest of 5 percent of the par value, or $50. The coupon rate doesn't ever change; as long as you own the bond you'll get $50 a year in interest. So if you had paid $1,000 for the bond -- par value -- you'd be getting a 5 percent annual return on your money. But say you'd actually paid only $950 for the bond. Then the $50 annual payment would represent a 5.26 percent annual return. If you'd paid $1,100 for the bond, the $50 annual payment would represent about a 4.55 annual return. Your "actual" rate of return is called the yield rate, and it's based not on the par value but on what you paid for the bond.
The market prices of bonds rise and fall to keep their yields competitive with similar investments. If similar investments offered a 5.5 percent annual return, for example, no one would pay par value for a bond offering 5 percent, because they'd be getting less money each year. But by cutting the price of the 5 percent bond, the seller can raise that bond's effective yield to make it competitive. Market prices and yields move in opposite directions: Cut a bond's price, and its yield rises; raise the price, and the yield falls. When a bond sells for less than par value, it's a "discount" bond. Bonds selling for more than par are "premium" bonds.