The reasons for developing a parallell system such as Galileo are obvious. GPS has been around for a long time and has it's limitations - the ability of it's owner to switch it off at will being a big one!
Galileo is far more advanced and will give far better accuracy. And it is in operation now. Only a few satellites are flying, but combined GPS/Galileo sets are on sale now and they use a combination of signal from all the satelites they can see - including Galileo's.