Net asset value

 (NAV) represents the market value of the component assets held in one share of a mutual fund, exchange-traded fund (ETF), closed-end fund, or unit investment trust. Because ETFs and closed-end funds trade like stocks on the stock exchange, their shares trade at market value, which can be a dollar value above (trading at a premium) or below (trading at a discount) net asset value.

Explanation for beginners
A mutual fund is a big package of "assets," often shares of stock. (Other examples of "assets" could be bonds, or "short-term commercial paper," or commodities like silver.) The mutual fund itself is divided up into shares. The NAV represents the market value of the assets in one share of the mutual fund. The absolute value isn't important, because you customarily buy mutual funds in any dollar amount you like; nobody cares just how a big piece each share is.

The actual list of assets the fund holds is listed in the "annual report" and "semiannual report" which are normally linked online from the same place where you get the prospectus. It is often worth looking at this list, although it can be pretty overwhelming for a total stock market fund that holds stock in 3,000 different companies!

If you go to a brokerage and say "Buy me $3,000 worth of (say) the mutual fund Fidelity® Growth Company Fund (symbol FDGRX)," since the NAV is $85.92, if you look in your account you will find that it tells you that you have 34.916 shares of the fund and that their market value is about $3,000.00. There's actually roundoff error, you may find that you've ordered $3,000 but received exactly 34.916 shares and it therefore cost you, and is worth, $2999.98 instead of a perfectly exact $3,000.

As the fund (hopefully) grows, you may look in your account one day and find that instead of $3,000 the holding is now worth $3,100. The NAV is important to understand here because that growth comes in two different ways. First, the market value of the stocks in the fund may have gone up, so each share of the mutual fund is worth more, maybe $88 instead of $85.92. Second, the stocks in the funds have paid some dividends, which the mutual fund itself distributes from time to time. Usually you have the fund reinvest those dividends, so those dividends have the effect of buying more shares, so that instead of the 34.916 shares you started out with, you now have 35.227.

Your fund holding is worth more because you have more shares and because each share is worth more. The NAV tracks the second part.

If you're a retiree or for any other reason, you can also tell the fund not to reinvest dividends. If you do that, the number of shares you hold stays exactly the same, the value of your holding reflects only changes in the NAV, and every so often, usually quarterly, the fund pays out a dividend, which typically gets paid into a money market fund that you've designated for that purpose.

Some quotes from the web
From Investopedia:

From a forum discussion:

Bond funds versus equity funds
Most Vanguard bond funds accrue interest to the share holders daily. Here is a typical statement from a prospectus:

The term accrue used in this sense means that the income dividends are credited to your account each day, just like interest in a savings account that accrues daily. Since the money set aside for your dividends is both an asset of the fund and a liability, it does not affect the calculated net asset value. When the fund distributes the income dividends at the end of the month, the net asset value does not change as both the assets and liabilities decrease by exactly the same amount. If you sell all of your bond fund shares in the middle of the month, you will receive as proceeds the value of your shares (calculated as number of shares times net asset value) plus a separate distribution of the accrued income dividends.

In most equity funds and balanced funds, dividends do not accrue to you; and you only become entitled to them if you hold the fund on the distribution date. Therefore, accumulated dividends are not liabilities of the fund; as dividends come into the fund, the net asset value increases. Only when the dividends are paid out does the net asset value decrease by the dividend amount.