Supply Is Based on Profit Maximization
One assumption in economics is that companies operate with the single explicit goal of maximizing profits. Therefore, the quantity of a good supplied by a firm is the amount that gives the firm the highest level of profit. The profit that a firm makes from producing a good or service depends on a number of factors, including the price that it can sell its output for, the prices of all of the inputs to production, and the efficiency of turning inputs into outputs. Since supply is the outcome of the profit maximization calculation, it's hopefully not surprising that these determinants of profit are also the determinants of the quantity that a firm is willing to supply.
Implicit Time Units
It doesn’t really make sense to describe supply without mentioning time units. For example, if someone asked “how many computers does Dell supply?” you would need more information in order to answer the question. Is the question about computers supplied today? This week? This year? All of these time units are going to result in different quantities supplied, so it’s important to specify which one you are talking about. Unfortunately, economists are often somewhat lax about mentioning the time units explicitly, but you should remember that they are always there.