Time Machine local backups
If you use Time Machine, my guess is that the discrepancy is from local backups. If so, you can free up that space by connecting your Time Machine drive and running letting Time Machine complete a backup.
Once you have done that, you might want to disable local backups by issuing this command in Terminal.app:
sudo tmutil disablelocal
but keep in mind that the local backups are meant to provide a safety net for those times when your Time Machine drive is not attached.
If the cause is not Time Machine, try OmniDiskSweeper
If that is not it, I recommend using OmniDiskSweeper to check your drive space.
ODS is a free app, and works very simply. When you launch ODS, it will show you a "Drive List" showing all of the available drives. Choose your main hard drive and then it will start searching.
The results are shown in a very simple column format, similar to the Finder. The largest folders will bubble to the top, and will let you see exactly where your disk space has gone.
Using OmniDiskSweeper as root
ODS will only calculate the sizes of the folders that you can read. 99% of the time, that should show you the problem.
However, if you want to be sure that you are seeing everything you can launch the app as root using this command:
BUT BE VERY VERY CAREFUL WHEN DOING THIS, since ODS will allow you to delete files.
If you have Time Machine Local Snapshots enabled (and I'm fairly sure it's enabled by default), then it's going to use some of your free space for creating these local snapshots. However, Finder doesn't take the space used by this feature into account, pretending it is actually free, because if the user starts filling up the disk, then the local snapshots get deleted -- it will only use `idle' free space, so to speak. See this other question for more details.
So, don't worry, if you actually need the extra space reported by Finder, then it will be made available to you when the need arises.
"Other" is all the files on your drive that aren't Audio, Movies, Photos, Apps, or Backup; in other words, all your documents and other saved files (and any media files in a format that System Information doesn't recognize as media files).
If you want to determine what files are taking up a lot of room on your drive, a tool like OmniDiskSweeper (free from OmniGroup) can help you identify where and what the files are that are taking up large amounts of space on your drive. Note that you might end up wanting to "clean it up" and you might discover that the space is taken up by files that you value and want to keep.