The float is the number of company shares in public hands and available for trading.
While you might think the float is the favorite summer-time drink of Wall Street, it is not. And, except for Yum! Brands A&W locations, the float has nothing to do with ice cream. The reality is actually a bit more boring, as is often the case when talking about stocks and investing. (But did you notice how I slipped in the name of a company?)
The float is the number of shares actually available for trading. It differs from shares issued and shares outstanding, which are more inclusive in their counts. The float does not include restricted stock owned by a company's officers and insiders. In other words, it is what the public can actually trade.
When calculating short interest or days to cover, it is the float that is used in the numerator.
The company itself rarely reports what the float is. That information is usually found on financial information websites such as Yahoo! Finance or Google Finance, or Morningstar or the Wall Street Journal's, to name a few.
Unless the company has been buying back a lot of shares and not retired them and, unless the company has a lot of restricted stock, the float will approximate the shares outstanding count.