Free float refers to those shares which are readily available for trading in the share bazar. It generally excludes promoter's holding, government / strategic holding and other locked in shares, which will not come to the market in normal course of trading. Thus the free float market capitalization of any stock is less than or equal to the full market capitalization of the stock.
It helps understand the traded volume of a stock better relative to the free float capitalization rather than the full capitalization. For example, two stocks having the same full capitalization and daily traded value may have different interpretations if 100% of the stock of one company is free float and only 1% of the same is free float for the second company. It would indicate a much higher trading and investment interest for the second company.
Hence, even for construction of share market indices, globally and domestically, free float market capitalizations are more frequently used as compared to full market capitalizations since it more accurately reflects the market movements in which the investor can invest as well.