The (share) volume of a given stock is defined as the number of shares of a security (stock, bond, etc) during a trading day. For instance, if NYSE reports the trading volume of AAPL to be 8 million, that means that a total of 8 million shares were bought/sold and were exchanged on that day.
Note that the volume does not directly indicate the dollar amount traded on that day. Suppose, on a trading day, 1000 shares of a certain company were sold, then bought back, then sold again and then bought back again at the same price, resulting in four trades, this registers a share volume of 4000. But if each share is, say, $2, then the actual dollar amount traded is $2 * 4000 = 8000$, whereas the share volume is reported as 4000.
Lastly, share volume indicates interest in a certain security. For example, if the average volume of a stock (say, AAPL) is 8 million, and on a certain day the volume rises to 30 million, this suggests a sudden spike in interest, usually caused by events such as good or bad earnings releases, a fraud case, or the leaking of an activist short position.
The average volume is defined as the mean of daily volumes of a security (stock, bond, etc.) for a specified period. So, if we want to find the average volume for the past 100 days, we would compute the volume values of the last 100 trading days and average them.
Average daily 10-day volume
The 10-day average volume is defined as the mean of daily volumes of a security (stock, bond, etc.) for the past 10 days. For instance, assuming AAPL had the following daily volumes the last 10 days:
[1M, 2M, 1M, 5M, 3M, 2M, 2M, 2M, 4M, 2M]
The average of that would be 2.4M. This means, the 10-day average volume would be reported as 2.4M.