Warped rotors should be replaced. Occasionally, they can be turned down to true again, but that leaves less mass on the rotors and a greater chance of failure again.
Typically, rotors warp due to uneven cooling. Unless you engage in opentracking or some other driving activity where the brakes get routinely pushed to the limit, I'd suspect you got the brakes really hot and didn't allow them to cool down to normal operating temps before shutting it down. As the excessively hot rotors cooled down, the caliper/pad assembly was static on the surface and didn't allow proper airflow to reach that area.
And you can drive on warped rotors but it is a safty issue. The capabilities of your brakes have been reduced and so you can't stop as well as normal. Under braking, that deflection is undoubtedly stressing the caliper and could eventually weaken its mount. It's a good idea to get it fixed as soon as you can, but it's not so bad that you can't drive it to the shop.