What does jailbreaking an Iphone mean?

If I jailbreak my Iphone 3g is it possible to download Instagram?

IPhone 3gs have no camera, and no matter if it is jailbroken or not, you can't take pictures.

iOS jailbreaking is the process of removing the limitations imposed by Apple on devices running the iOS operating system through the use of hardware/software exploits - such devices include the iPhone, iPod touch, iPad, and second generation Apple TV.
IN ENGLISH: You remove all of the blocks that prevent you from downloading apps that apple doesn't like.
Like Adobe Flash Player and things by nintendo.

To answer your question, yes.
But I woulnd't consider jailbreaking your phone. Yes, Jailbreaking your phone allows you to download free apps/music/etc… But it can also cause a lot of problems. If your phone has a problem, employees are not allowed to help you/Apple company can't replace your phone anymore. And Jailbreaking is illegal

Jailbreaking is not illegal ^. But, anyway, when you jailbreak your iphone you basically unlock every feature on there. For example, you can get very cool animated themes, flash player, free apps, free music, free in-app purchases. And if you r a hack and can program you can do anything you want with your iphone.

Jailbreaking is basically making your iPhone capable of running software from other sources and do more than what the phone was designed for, such as iOS 5, wallpapers behind icons, and such. So yes you will be able to use instagram, but your phone is basically unstable after this, and not supported. Plus, you can seriously damage your system if you don't know what you are doing.