It could be Time Machine Snapshots
<About Time Machine local snapshots - Apple Support>
OmniDiskSweeper (free download)
<http://www.omnigroup.com/more>
DO NOT delete files in your Home Folder -> Library tree as there are things like your iPhone backups, your email messages, your application preferences, etc… If you think you have found something in your Home Folder -> Library that can be deleted, you should ask first.
DO NOT delete files outside your home folder, as you may end up deleting something essential to Mac OS X, and turn your Mac into an expensive “Door Stop”.
I will point out that you will find some very large files in private -> var -> vm (these are the Mac OS X virtual memory paging files (swapfiles) and where Mac OS X stores the copy of RAM when your Mac is put to sleep). The swapfiles get deleted on reboot, and the sleep image is just going to be created again when you put your Mac to sleep.
If you think you have found something to delete outside your home folder, it would be best to ask first before deleting. There are many examples of people deleting files outside their home folder, or renaming files, or changing the ownership or permissions of files, and then their Mac stops running. Do not be one of those people. Ask first.