For a mutual-fund the NAV is the price: orders placed during the day all execute at the NAV struck after the close. For an etf or a closed-end-fund the NAV is a reference value while the market price is set by trading, which is what makes a premium-discount-to-nav possible.
NAV is only as good as the marks behind it. Funds holding illiquid or foreign assets carry stale prices between calculations, which is why an international fund's NAV can look wrong when the underlying markets are shut.
Example: a fund holds $812M of securities, $6M of cash, and owes $3M in accrued fees, across 40M shares. NAV is ($812M + $6M - $3M) / 40M = $20.375 per share.
Related: premium-discount-to-nav, etf, mutual-fund, closed-end-fund, creation-redemption