The cause of the crack is expansion of the brick usually from sunlight or summer heat. The brick is usually a different color than the white concrete foundation and therefore expands and contracts at a different rate than the concrete. During the heat of the summer the brick “slides” or elongates more than the concrete foundation and therefore “pushes” or breaks the corner off the foundation from the expanding brick.
The corner concrete foundation crack is unsightly but usually not a big problem unless the brick is cracked above the corner. If there is a gap in the cracked brick above the corner you will need a brick mason to make this repair.
You can repair this broken concrete corner by gluing it back together with a clear two-part epoxy. Mix the epoxy and apply it to both surfaces of the concrete corner, apply the corner back into its original position and hold it there for about 10 minutes for the epoxy to quick-set. This clear epoxy will usually do the trick.
After the corner is fully cured for 24 hours you can tuckpoint between the concrete foundation and brick to better support the brick. Install a 30 mil plastic “slip sheet” material or thin copper sheet as a gasket on top of the concrete foundation for the brick to slide on. Then tuckpoint the mortar between the concrete and the brick.