The market cap (market capitalization) of a cryptocurrency is the total dollar value for all the coins in the marketplace. So, if you multiply the current price by number of coins that have been mined upto now, you have the market cap.
The market cap is a strong indicator of how much demand and value a certain cryptocurrency has. Cryptocurrencies with a large market cap are usually more stable and thus won't lose much value easily. For instance, while Bitcoin may drop 50% in an event of large-scale deleverage in the cryptocurrency space, small-cap coins may at the same time drop up to 99%. Today Bitcoin has a market cap of 814 billion dollars, which is not too far away from the market cap of the largest public companies on the US stock market (e.g. AAPL or MSFT). The market cap of some of the smallest cryptocurrencies are in the low thousands. For those, in theory on could just buy all the outstanding coins.
In the traditional sense, there are often denominations such as large-cap, mid-cap, small-cap, micro-cap and nano-cap. Since cryptocurrencies are evolving rapidly, it is likely too short-sighted to adopt the same denominations (with the same thresholds), but it is likely that at some point there will be clear definitions here, too. It is however pretty clear that the largest cryptocurrencies (such as Bitcoin) can be seen as large-cap, especially when looking at the historical price action.