Discarding order is when you Right Click ---> Orders and discard all or some of them. Do this for 1000 orders. They will come back after a short time. Get achievements for 100, 500, and 1000.
There is absolutely no reason to do this when playing regularly. You should start this at the beginning of your career, and you should be done by the time you finish all story orders or shortly after. Just be sure to check back every 3-5 minutes or sooner and discard all the orders you don't want to do.
Some helpful information for the entire game, and also deciding which orders to decline:
There is no circumstance ever where you should want to accept order with more than ONE thing wrong with the cars. (This means only accept orders with ONE light illuminated; either Exhaust, Transmission, or Brakes.)
1. Exhaust is by far the best if you can get this. Sometimes they can be completed in under 30 seconds if it's just a couple of exhaust pipes under the car. Otherwise, a little over a minute.
2. Transmission is the second best. Simply because the same thing is wrong pretty much every single time. (Gearbox, the three clutch parts, and the flywheel) and if you get a V8, this can be done in about 1.25 minutes. If you don't, it may take up to 2.5-3 minutes. This is because on a V8 the starter is underneath the car and also you don't have to disassemble the wheels and axles to reach the gearbox.
3. Brakes. Only accept as a last resort. This can take 5-6 minutes to do, but if it's all you got, go ahead and do it. You will more than likely have to take off all four wheels and calipers/pads/discs. There also may be something wrong with the ABS module/pump.
So basically, discard all orders that aren't exhaust only, transmission only, or brake only. And check back frequently.