There is a number beside the current bid price and a number beside the current ask price. Do these numbers represent the volume of trades completed at the bid and ask prices or pending completion?
The numbers that you are referring to are the bid and ask volume and they represent the size of the market at current price.
For example, the current NBBO is $10 x $11 with a size of 8 x 7. That means that one or more people are looking to buy 800 shares at $10 and one or more people are looking to sell 700 shares at $11.
If you were to place an order to buy 500 shares at $10.25 then the quote would become $10.25 x $11 with a size of 5 x 7