The two cent piece was very popular for a short time. From its start in 1864 it was used very often because Americans didn't want to deal with pennies and the nickel wouldn't be made for another two years. Unfortunately less and less two cent coins were minted every year till their complete termination in 1873. The new nickel and three cent coins made it unnecessary.
The two cent coin and the first nickels have virtually the same “shield” design. If it looks familiar that may be because it is the shape of a route sign. Above the sign it says “IN GOD WE TRUST” for the first time ever on an American coin. The reverse has a wreath similar to one on a flying eagle.
My coin is in VG (very good) condition and worth about $15. It is considerably larger than a penny. Unlike silver coins, its melt value doesn’t exceed much past its face value. Picture citation: https://www.coincommunity.com/coin_histories/two_cents_1864.asp