The jet stream, a fast moving current of air above our heads, has been shown to get stronger both in terms of its average speed but also its fastest days in climate model predictions. Here assuming a moist atmosphere whose temperature structure is only influenced by cooling from expansion and heating from condensation of moisture evaporated from the ocean surface we explain why the jet stream strengthens. We show that following this assumption the jet stream gets stronger by 2% per degree of surface warming and the shear of the jet stream (how its strength varies with altitude) gets stronger by 4% per degree of surface warming. Both changes are the result of warmer air on the equatorward side of the jet stream ``holding' more moisture under climate change. The results show record-breaking upper-level jet stream wind and increased clear-air turbulence are tied to warmer air ``holding' more moisture and are therefore robust and well-understood consequences of climate change.