Check out the picture, Vayden. It shows two different minting errors, one called broadstrike and one called die cap. Both errors affect the rim of the coin. The errors shown are pretty dramatic, and therefore command numismatic value. Approximate valeus for each of the coins in the picture is $10 to $25 US dollars. Older coins, larger denomination coins, or errors that are more dramatic, would command higher prices. Here is a summary:
COINS FROM 1900s and 2000s:
raw: $10 US dollars approximate catalog value
in numismatic slab, fully uncirculated: $50
COINS FROM 1700s and 1800s:
raw: $50 US dollars approximate catalog value
in numismatic slab, fully uncirculated: $350
A broadstruck coin occurs when the minting press loses the collar that encircles the raw metal while it is being hammered between the presses, i.e., the dies. Without a collar, the metal oozes outward.
A die cap coin is one that gets stuck on the die and gets hit multiple times as the press operates. A die cap ends up looking like a bottle cap, with a rounded shape.
There is a chance, however, that coins like this were damaged by some circular scratching after the coin came out of the mint. If this is the case, the value of your coin plummets to about zero. Only errors during minting, not after-mint damage, counts when it comes to numismatic value.
Thanks to Mike Byers for his excellent work on minting errors.