What is Mobile Sync - Backup and why is it taking so much space?
It's the folder where iTunes saves the backUps of your iDevice. And it takes so much space because each time you sync a device, previous backUps are not deleted. 

Deleting the folder will, then, mean losing those backUps. Doing this regularly is advised for saving HD space. Just make sure to make a new backUp afterwards, and that you won't need those backUps.

You can do that through iTunes too, by:


Opening iTunes / Preferences / Devices.
A list with all the Devices will be show. Select the one's backUps you want to delete and click Delete Backup. 


Note that all of the backUps of that iDevice will be deleted.