when people talk about getting "root" access they are basically talking about jailbreaking a phone. the term jailbreaking seems to stick with apple products but other phones call it "rooting" or "getting root access".
for what you're trying to do (you don't mention which model) it should be fairly simple. just find which model and use an appropriate app, spirit is fairly simple, to perform the jailbreak and install the Cydia application manager (it's similar to the app store application). then install the latest unlock application available at the time (redsn0w, blacksn0w, the name changes). reboot your phone and you're generally done. you don't ever have to launch cydia or worry about other jailbreak applications if that's all you want to do. but if you ever get curious you can browse the Cydia repository and see what else they offer. everything from lock screen widgets to different themes, ringtones, security software (like Firewall IP), games, etc.
the android source code is available from google. apple will never release the iOS source code to the public.