As I recall, it (i.e. the polar front jet stream in the Northern
Hemisphere) is driven by the upper level pressure gradient at the
polar front at the boundary between the midlatitude Ferrel cell and the
Polar cell caused by the tropopause having a near discontinuity in its
height at the boundary. (The tropopause is lower for the Polar cell than
it is for the Ferrel cell, and that is lower than the tropopause is for
the tropical Hadley cell because of the difference in temperatures of the
air circulating in each of those cells. Cold air is denser than warm air
and the tropopause is correspondingly lower.) This difference in height
of the tropopause across a relatively narrow transition zone results in
a strong upper level horizontal pressure gradient where the high
pressure is on the southerly side and the low pressure is on the
northerly side of the transition region. This pressure gradient is
essentially due to the fact that at the appropriate upper level height
there is a higher fraction of the troposphere's mass and weight stacked
up above that height on the south side than on the north side. This
pressure pushes a band (in altitude) of upper level air poleward
(S to N in the N.H.) As this air begins to pick up speed the Coriolis
force acts to deflect it to the right (eastward) and the strength of this
deflection force increases with the wind speed. A quasi-steady state
rapidly ensues where the air stream is flowing essentially eastward at a
constant velocity where the northward directed pressure gradient force is
completely compensated for by the southward directed Coriolis force.
This band of moving air is sort of a hydrodynamical version of the Hall
effect (with the magnetic force mapped to the Coriolis force, the
pressure gradient force mapped to the electric force, the air current
mapped to the electric current, etc.).
There is also a jet stream arising from a similar situation that occurs
at the boundary of the Hadley cell and the Ferrel cell. I believe there
are also corresponding jet streams in the Southern Hemisphere as well
(except for them there are the usual inversions of the relevant polarites
of the Coriolis force and the North-South orientation of the associated
phenomena).