Trading volume is the number of shares that changed hands over a given period — a day, an hour, whatever the chart's interval is. It's usually plotted as a bar beneath the price chart, one bar per period.
Volume is a rough proxy for how much conviction is behind a price move. A large price jump on unusually high volume is generally read as more significant — more participants agreeing on the new price — than the same-sized move on thin volume, which can reverse just as quickly since fewer buyers or sellers were actually involved.
Volume also matters practically for how easily a position can be entered or exited: a highly liquid, high-volume stock can typically absorb a large order with little effect on price, while a thinly traded one can move noticeably on comparatively small orders. See "most active" on the markets page for the day's highest-volume names.