Booting to your recovery partition means using the built in recovery utilities to: Verify and repair the hard drive if necessary, re-install the operating system, do partition work, and so forth. In other words, doing things to the hard drive which requires that it not be mounted.
The last three operating systems from Apple (Lion, Mountain Lion, and Mavericks) are not available on disk and so Apple provides a way for you and I to do repairs and maintenance on the hard drive without an external disk. In order to accomplish that, the system has to be booted to recovery. We can do that by holding down the "R" key and "Command" key during the boot process.
Yes to making a Time Machine backup. Additionally, we recommend using cloning software to make a bootable clone of your system. Time Machine backups are not bootable whereas a clone backup is. The two applications recommended are:
Carbon Copy Cloner and
SuperDuper.