From Traderpedia

Definition: The number of units (shares, contracts, etc.) immediately available to buy (bid) or sell (ask).

For example, if one were to buy 100 shares, the size would be 100. Likewise, if a bid-ask/offer quote is 100 (50,000)- 100.50 (100,000), the size of the bid is 50,000, while the size of the offer is 100,000.