Supply, in simple terms, is the amount of a product that will be available at a particular price, and the law of supply states that more will be made available when the price is higher. For example, if the iPhone costs $90 to make and apple is allowed to charge customers $400-$500 to buy the phone, more will be made. But if the phone cost $300 and Apple can still only charge $400-$500, less iPhones would be made because they wouldn't bring in much of a profit.
When bringing supply and demand together, like on the video, both the supplier and consumers point of views are brought into the picture and things get a bit more complicated. When quantity of whats demanded meets the quantity of what is supplied a market equilibrium is met, which looks like this. But when one changes, supply for example, everything changes over time. If the price of drilling and refining oil goes up, the supply line on the graph will change. In this example, the supply line would move to the right, thus causing the quantity of supply at the original price to decrease. Meaning before $2.15 would have gotten you a gallon of gas, but now it only gets you half. This also causes the original equilibrium to move up.
There are several factors that could cause the supply line to shift in a market, such as change in cost of inputs, taxes and subsidies, change in the amount of sellers, future expectations, etc.