The jet streams in our rotating (spheroid) planet meander because they cannot maintain a straight zonal course. The atmospheric flow is effectively perturbed upon collision to large mountain ranges like the Rockies and the Himalayas; an effect that is also felt at the jet stream level (i.e., around 10km above ground; upper-troposphere). The inhomogeneous temperature field due to land-sea contrasts and the latitude-dependent insolation results in an inhomogeneous pressure field that gives rise to winds of any direction and eddies. Convection, clouds and precipitation can also affect the upper-tropospheric flow.
All these reasons can provide a "kick" in an initially zonal jet. This "kick" means that air masses will move toward different latitudes to the north and south maintaining the vorticity of their original position (since vorticity is conserved under certain assumptions). Cyclonic/anticyclonic rotational movement thus emerges and the jet develops the so-called Rossby waves. These waves are highly-dynamic flow features with a shape and propagation that evolve constantly and give rise to the meandering of the jet that hosts them. Since some regions in the midlatitudes are baroclinically highly unstable (i.e., the meridional temperature gradient is large and small eddies can quickly grow bigger), these meanders are often rather pronounced and the meridional component of the wind dominates the zonal one.