In a stock quote, the ask price is the price at which the seller is willing to part with his or her shares. The listed ask price on an exchange is the lowest price at which any seller is willing to part with his shares.
When the bid price is equal to the ask price a transaction occurs.
Anytime someone wants to sell a stock they own they can place a price on that stock and put it on the market through a limit order. The price they set is their asking price for the stock. A market for purchasing a stock is created by many people listing the price at which they are willing to sell their stock. If someone places a market order to buy a stock they begin buying shares at the lowest asking price. When all the shares at that price are bought they begin buying shares at the next highest asking price. This is how the price of shares goes up as people buy.