Auto boot = to boot automatically. I.E. you turn on the device and it does everything it needs to start running. Most computers do it these days, because the OS is in the hard drive.
A boot disc (or boot disk) is an external drive (floppy disk, CD, DVD, pen drive, etc.) that has an OS (operating system) and loads it when you start your device with the disc inside. For example, a live CD/DVD.
I remember back in 1992 when I was taught how to make a DOS boot disc. You had to insert a floppy disk in drive A: and then enter the command "sys A:" (alternatively, you could use another letter if you had more than one floppy drive).
Now the most common way to get a boot disk is to download an ISO image and burn it into a CD or DVD.