Recovery mode is very useful and there are a lot of features you can use from there. Especially if you have ClockworkMod Recovery installed, there are a lot of useful features.
In recovery mode you can factory reset / wipe data, wipe cache and dalvik cache on your Galaxy S3. In recovery mode you can also install updates, custom ROMS of kernels very easily. And there are some other features you can find there too, like reformat partitions, fix permissions, mount or unmount partitions, and connect the USB storage.
If you want to get ClockworkMod Recovery ( CWM ) on your Galaxy S3, then here's a guide to flash it.
We also have a guide to enter download mode and you can find it here.
How to enter recovery mode on Galaxy S3 i9300
Entering recovery mode on Galaxy S3 is very easy. All you have to do is shut down your device and boot while holding the volume up, home button and power button simultaneously.
We also have a video that shows you how it's done. You can watch it below: