The answer has been supplied several times already, but for some reason nobody knows it when they see it. And posters claiming that it's a dodge used by people to sell warped cues are correct. Fact is people generally misunderstand it. Worse yet, folks use the term to describe a warped cue so they can sell it. It sounds nicer than "warped" and sounds technical so it confuses people into thinking it's actually straight when it's not. Some, I assume, are innocently ignorant & just passing false info. Rarely do I see somebody use the term correctly.
Take a rod & give it a cam shape instead of a perfect circular shape. Roll it. No matter how straight it is, it'll wobble. Take three or four perfectly round components & join them straight but slightly offset from center, with the front & rear components being on the same center line. The assembled unit will be straight but when rolled, it'll wobble. Is a crank shaft straight? You bet it is, or it wouldn't work. But it will wobble horribly if rolled flat. Between centers it spins fine & smooth and straight. Water down the crankshaft & /or cam effect and apply it to cues and you have true taper roll. It's not warped, or non-straight. But it won't roll straight. It's pretty simple.
This simple explanation is what builders who use compound tapers use to explain why cues don't roll straight on a table. Somewhere along the way, people borrowed the term & applied it to slightly warped cues so they could sell them with minimal loss of value. Nowadays when you see a cue listed and "taper roll" is in the description, there's a very good chance that it's a warped cue. The most common taper roll is joining shafts to butts. They both may be dead straight, faced dead flat center, but the pin or shaft hole may be a couple thou off center, meaning two very straight components join slightly off center, but are still faced straight. When blended together, one or both of those components will become out of round. That cue rolled on the table will show variance in the light under the shaft as it rolls, even though it's perfectly straight. Saying it's warped would be inaccurate. "Taper roll" would accurately describe the variance you see in the shaft taper, would it not?
makes perfect sense to me,,,,,,,,