Band bending refers to the local changes in the energy offset of a semiconductor's band structure near a junction, due to space charge effects. Because the common way to visualize the electron energy states and Fermi level in a material is to draw bands on an energy vs. distance plot (band diagram), band bending refers to bending observed in these diagrams and does not correspond to any physical (spatial) bending.
The primary principle underlying band bending inside a semiconductor is space charge: a local imbalance in charge neutrality. Poisson's equation gives a curvature to the bands wherever there is an imbalance in charge neutrality. Why is there charge imbalance? Although one expects a homogeneous material to be charge neutral everywhere (since it must be charge neutral on average) there is no such requirement for interfaces. Practically all types of interface develop a charge imbalance, though for different reasons:
Knowing how bands will bend when two different types of materials are brought in contact is key to understanding whether the junction will be rectifying (Schottky) or ohmic. The degree of band bending depends on the relative Fermi levels and carrier concentrations of the materials forming the junction. In the p-type semiconductor the band bends upward, while in n-type the band bends downward. Note that band bending is due neither to magnetic field nor temperature gradient. Rather, it only arises in conjunction with the force of the electric field.