OS X Base System is the recovery partition (used to install OS X without a CD).

To use it just boot into Recovery Mode by pressing Command+R when starting the system.

You’re going to want to use disk utility and format Macintosh HD.

How do I uninstall OS X base system in Disk Utility?

Removing the partition with Disk Utility by formatting the disk

• Boot the Mac from a recovery DVD, USB key, or an attached drive.
• Launch Disk Utility.
• Right-click on the Disk (not the partitions) and select “Erase”
• Select the default Mac OS Extended (Journaled) as the file system, and give the drive a name.

Should I erase my OS X base system?

Should I erase OS X Base System? Answer: A: Answer: A: There is no need to erase The Base System.