Market cap of a coin determines its value. If the market cap doubles, the value also doubles. Circulating supply is also important in doubling the price of a coin. Market cap and circulating supply together determine the price of a coin. Other factors are valuable but these two are most important.
Marketcap does not reflect value of a coin but it reflects current price of that coin.
Current price can be higher, lower or as same as value of the coin. You can not say a value of Dogecoin is at $0.7 when it pumps to that price within a few hours. It is just a temporary price and temporary marketcap for Dogecoin.
Its value is determined by its use cases, usability and how small or big its adoption is, its communities are and more factors.