The (as)Authorized shares are the most a company can issue into the market shares(os ) - currently in the market
the float is the os - minus restricted shares held by insiders, etc. Another words only tradeable shares
For example , stock abcd
As is 5,000,000,000
Os is 1,300,000,000
Float is 1,000,000,000
The float is 1b
There are 300,000,000 restricted shares
However 5b(as) - 1.3b(is) = 3.7b shares left to dump into the float = dilution.