Thermal wind is wind that varies with altitude (generally stronger at a higher altitude) due to a horizontal pressure gradient varying with altitude, in turn due to a horizontal temperature gradient. It is a type of geostrophic wind (the component of the wind created by a pressure gradient and the Coriolis force), specifically that can occur when the underlying pressure gradient is due to varying temperature. The wind is said to be thermal because a temperature gradient made the winds faster as you go up.
Typically air is warmed more the nearer to the equator, and the expanded warm air results in a higher pressure at any given altitude, and the greater the altitude, the greater this effect. The air tends to move horizontally from the high pressure area toward the low, the greater the altitude, the harder the "push". The Coriolis force (apparently) turns the wind, such that a north-south difference in temperature (and pressure) results in a wind in an east-west direction: on Earth, toward the east if the air that's further from the equator being the cooler.
These "winds" represent just some of the forces on actual air movement, in particular, ignoring friction with the surface (ground), but they allow for tractable equations describing the winds. In some portions of the world, i.e., where geometry makes the Coriolis effect pronounced, the factors in this model are significant and may accurately model actual weather. An atmosphere moving according to the model is said to be in geostrophic balance if they match the equation describing geostrophic wind, and in thermal wind balance if they match the equation describing thermal wind.
The jet stream, a high-velocity, high-altitude west-to-east wind is a result of thermal wind.