Are you on a Mac?
You need to google "creating an aggregate device"
Your computer has inputs (probably a mic) and outputs (its built in speakers). The AXE III is an 8x8 USB device.
What you need is to meld them together to create a virtual device that has all of those ins and outs.
In that way, when you open your DAW and choose the Aggregate device, you will be able to put audio, or receive audio from either source (computer or Axe) and send it to either device.
Without the Aggregate Device, your DAW probably chose the AXE III as the sound source, and you need to be able to also have your computer speakers - you probably don't actually need the built in mic of your computer to be included in your Aggregate device, but you can figure that out yourself.