A thermal bridge is a fancy name for a simple concept: where a building has less insulation, there will be more heat transfer.
Also known as a cold bridge, a heat bridge, or thermal bypass, a thermal bridge is a weak spot in a building's thermal envelope, where heat can get in and out of the building more easily. This is a concern because heat transfer is a cause of discomfort and increased energy bills, and also because having unplanned cool spots in a structure can lead to condensation, mold, and damage to surfaces, structural elements, and existing insulation.
Thermal bridging results from inconsistent insulating, especially at wall/ceiling junctions and metal or masonry elements that pass through or abut better-insulating materials. The unfortunate necessity of windows and doors also leads to thermal bridges, which may be addressed by triple glazing and vestibules, among other things.
Thermal bridges are intrinsic to the structure, but there are other factors that lead to inconsistent temperatures. For example, solar loading caused by the sun -- and the resulting shadows created by surrounding structures -- can cause significant variation in heat transfer, but this is not due to thermal bridging.