can I upgrade from OS X 10.4.11 ?

Hello,

Well, we bought an used mac for our daugther, we have never had mac so I didn't know too much about mac. Finally I enter to see what are the incredible things mac can do and windows cannot, for my surprise this mac doesn't even can install itunes, that means I can't enter into apple store??? and I can't install messenger either, less talk about xcode etc... The system is Mac OS X 10.4.11 , my question is, is this version too old? can't be upgrade to a Lion (whatever)? or did I paid too much (even used) for a Mac only to whatch movies? I think is 2007 but we bought it end last year (2012).

Thanks