When I first started building houses, in 1980, the standard wall construction was 2×4 studs on 16-inch centers. Ed Mazria had just published The Passive Solar Energy Book and the back to the land, small is beautiful, live simply scene was in full flower. I understood what R-values were (resistance to heat flow) and that we needed insulation and better windows. I understood the basics of south-facing windows and thermal mass to absorb the direct solar heat but had not heard of a thermal bridge much less a thermal brake. We did not know about the more subtle effects of thermal forces or moisture movement. My passive solar house got warm in the sun and cold without it.

As people began to understand that energy had significant costs both in terms of dollars and to the environment, building began to change; as the value of building an efficient envelope to maintain comfort with the least amount of energy for heating and cooling became obvious, Building Science took off. One of the first steps was to use 2×6 studs instead of 2×4 to allow more insulation and to use 24-inch spacing instead of 16 inch in order to use less lumber and allow for more insulation. This is one place where thermal bridges show up. A thermal bridge is created when materials create a continuous path across a temperature difference, in which the heat flow is not interrupted by thermal insulation. (Wikipedia)
This is a thermal image of thermal bridging.

Insulation has R-values of 3 to 6.5 per inch, whereas wood has an R- value of about 1.25 per inch. In 2×6 wall cavities with R-19 insulation, studs with an R-value of 6.8 will lower the overall insulating effects of your walls because the studs connect (or “bridge”) the interior conditioned space and the exterior climate. The effect of the framing factor on the standard wall insulation value is around 27%. A standard wall insulated with R-13 insulation will have a whole wall R-value of 10.
There are several ways to break the bridges or interrupt the heat flow from where you want it to where you don’t. Using advanced framing is a good strategy to minimize the number of bridges in your building envelope, and to reduce the amount of materials needed for the structure.
Another common practice to eliminate thermal bridging is to add a layer of ½- to 4-inch-thick rigid foam on the outside of the walls. Determining the appropriate thickness involves many factors, from cost to condensation. In Western North Carolina, a 2-inch layer of exterior rigid foam with an R-value of 10 is commonly recommended. Energy modeling can help you make a decision based on your local climate.
Another method is to build a double wall system with offset studs; this allows for thick walls and higher insulation levels while avoiding the bridges of continuous wood studs.
Other systems to reduce thermal bridging are: SIPS or Structural Insulated Panels that are usually OSB outer layers with rigid foam cores, insulated concrete forms, and most recently, hempcrete (http://www.hemp-technologies.com/ ) up to 16 inches thick that’s formed around the framing.
If you want to raise your energy efficiency and lower your energy costs, breaking the bridges is an important detail to address, not only in walls but in all areas where conditioned space connects to the outside, such concrete slab edges and windows.