There's nothing fancy about them. Some minters make copper rounds (a name taken from "silver rounds" - silver sold in a round shape like a coin, but it's not an official coin from any government).

They are typically replicas of coins made from 1 ounce of copper, although there are a lot of commemorative and fantasy designs. Half-ounce rounds are also becoming more popular. 1-ounce rounds are approximately the size of a silver dollar and were originally offered as a low-cost souvenir. Some touted it as a low-cost bullion investment when copper prices were on the rise, but their pricing at that time (higher than $3) hardly justified them as investment-grade.

I typically pick up the ones that replicate the designs of Lincoln pennies. I saw many at last week's Schaumburg coin show in the $1-$3 price range. The ones with the Bitcoin logo are not as common as some other designs, but they sell on Ebay for about $3 each. I once bought a roll of them and resold them for $4 to $5 as a novelty item.; the prices have come down as copper rounds have become more prevalent. Yours is different because of the painted logo, but since these are primarily a novelty item I wouldn't use words like "rare" or expect a big increase in value due to this feature.