AMC is active mining corporation, a company who purchased a load of avalon miners, which you can buy shares for and share the profit..
AMC American Coin is a new coin it looks like, based on litecoin it rewards 100 coin per block.
The question the op asked was what does 'there are xx blocks left until coins will be rewarded.' mean
I can only assume the network is currently open for mining but you will not be generating any coin until the timer hits 0, this is to give miners a chance to setup their rigs in anticipation of release. Rather than for the makers to start mining before anyone else has the chance thus pre-mining a ton of blocks