The Local Snapshot is for laptop users who may not be continuously attached to a hard drive over Firewire or USB and now Thunderbolt connections. The Mac continues monitoring changes made to the local hard drive (every time a file is opened or saved or downloaded) and saves all the changes into the 'local snapshot'.
Here's a Apple FAQ on local snapshot for your personal reading time:
http://support.apple.com/kb/HT4878?viewlocale=en_US&locale=en_US
On portable Macs, local snapshots are automatically enabled when you turn on Time Machine. Just like regular Time Machine backups, local snapshots are made hourly in the background.
Note: The Time Machine status in the menu bar does not change when a local snapshot is created.
Local snapshots are periodically condensed into daily or weekly snapshots to minimize the space used on your disk. If your disk is low on space, Time Machine stops creating new snapshots, and some or all existing snapshots may be removed to make space available for applications to use. If sufficient disk space becomes available again, Time Machine resumes creating local snapshots. This means your disk will have the same amount of available space as it would if Time Machine were not enabled.
When you enter the Time Machine browser (used to restore data), local snapshots will appear on the timeline along with regular backups distinguished by different colors. Gray tick marks represent local snapshots and pink tick marks represent backups stored on your external backup disk or Time Capsule. Note: Pink tick marks will be dimmed if your portable computer is not connected to your external backup disk or Time Capsule.