Under the US system you can (and many faculty do) typically arrange to have your nine month salary paid out in equal installments over the whole year.  If you do this then any summer salary you can arrange (e.g. from research grants, teaching summer school classes, or administrative work) is "extra" money.  Most faculty that I know budget to live off of their nine month salaries and then use the summer salary to invest into their retirement funds or to pay down their home mortgage or whatever.    

There are some advantages to the faculty member in having a nine month contract.  For example, you're free to use the summer to go on vacation or work for some other employer (lots of consulting work gets done over the summer.)  Working on research contracts and summer school teaching are optional.  The down side to this system from the point of view of faculty members is that there is no guarantee that you'll be able to get a full three months of summer salary.  

From the point of view of university administrators, the advantage of the 9 month contract is that it helps to keep salaries down in comparison with 12 month salaries in industry.  Universities don't need faculty to teach much during the summer, so why pay unneeded employees?  

Note that fringe benefits (like health insurance, life insurance, etc.)  cover the entire year including the summer when the faculty member is not on contract.