Cause
Jet streams can be explained as follows. In general, winds are strongest just under the tropopause (except during tornados, hurricanes or other exceptional situations). If two air masses of different temperatures meet, the resulting pressure difference (which causes wind) is highest at those altitudes. If one of the air masses lies north of the other one, then the wind will not flow directly from the hot to the cold area as one would expect, but is deflected by the Coriolis force and flows along the boundary of the two air masses.
All these facts are consequences of the thermal wind relation. The balance of forces on an atmospheric parcel in the vertical direction is primarily between the pressure gradient and the force of gravity, a balance referred to as hydrostatic. In the horizontal, the dominant balance outside of the tropics is between the Coriolis force and the pressure gradient, a balance referred to as geostrophic. Given both hydrostatic and geostrophic balance, one can derive the famous thermal wind relation, stating that the vertical derivative of the horizontal wind is proportional to the horizontal temperature gradient. The sense of the relation is such that temperatures decreasing polewards implies that winds develop a larger eastward component as one moves upwards. Therefore, the strong eastward moving jet streams are in part a simple consequence of the fact that the equator is warmer than the poles.
The thermal wind relation does not immediately provide an explanation for why the winds are organized in tight jets, rather than distributed more broadly over the hemisphere. There are two factors that contribute to this sharpness of the jets. One is the tendency for developing cyclonic disturbances in midlatitudes to form fronts. A front is a sharp localized gradient in temperature. The polar front jet stream can be thought of as the result of this frontogensis process in midlatitudes, as the storms concentrate the north-south temperature contrast into relatively narrow regions.
An alternative explanation is more appropriate for the subtropical jet, which forms at the poleward limit of the tropical Hadley cell. One can visualize this circulation as being symmetric with respect to longitude. Rings of air encircling the Earth move polewards beneath the tropopause from the equator into the subtropics. As they do so they tend to conserve their angular momentum. But they are also moving closer to the axis of rotation, so they must spin faster in the direction of rotation, implying an increased eastward component of the winds.
The polar front and subtropical jets merge at some locations and times, while at other times they are well separated. Historically, it was originally thought that the polar front was a structure that had an existence independent of the cyclonic eddies that, it was suspected, form as instabilities on this front. The modern perspective is that the cyclonic eddies are best thought of as growing from the store of potential energy in the broad north-south temperature gradient by a process known as baroclinic instability, and that the resulting extratropical cyclones then concentrate the gradient into a front, thereby creating the polar front jet stream.