Coin appraisal, also known as grading, is the process by which a coin is professionally evaluated in order to determine its real value. Grading compares a specific coin to an ideal example of that coin, creating a sliding scale of sorts that's based on the most perfect representation of that specific mintage.
Several professional coin grading organizations exist, offering hobbyists many opportunities to have their coins appraised and assigned a value. The actual value that a coin has is a function of its age, scarcity, the presence of errors during the minting process and its overall grade. As a result of the popularity of coin collecting, the U.S. Mint offers many coins in uncirculated form, making newer coins easier to come by and thus less valuable.
Older coins, especially those which had a limited number created, often have greater value. Unique or exceptionally rare coins include copper pennies minted in 1943 or steel pennies minted in 1944. This is because copper was needed to produce shell casings in 1943, so the U.S. Mint switched to zinc-coated steel for all pennies created in that year, then back to copper for 1944 minting. Mistakes happen though, and a limited number of copper pennies made it into circulation in 1943. The reverse occurred again in 1944, making those accidentally minted pennies worth substantial amounts.