A beak occurs during sharpening when the corner of your grinding wheel (or file) is not aligned with the outside corner on the face of a chisel cutter tooth. When the corner of your grinding wheel hits high in the tooth, it creates a top-beak. When it is low, it creates a side-beak. Below are the consequences of both types of misalignment.
Cutter teeth with side-beaks usually cut well, but they don't stay sharp as well as a tooth with perfect corner alignment. The beaked portion of the cutter tooth can be very sharp, but is weak because it is not well supported by the rest of the tooth. Even a hard knot will sometimes blunt the corner on side-beaked cutter teeth, making the chain dull.
People who sharpen with a file almost always cut a side-beak in the cutter teeth on their saw chain. They do this because it is so difficult to perfectly align the outside corner in the cutter tooth with the corner on the file. They know not to cut a top-beak under any circumstances, so they file a little low. This is a good idea, but it is also one of the reasons why ground chain usually stays sharp longer than filed chains. Perfect corner alignment makes for cutter teeth that cut well and stay sharp..
Cutter teeth with top-beaks won't cut. Some have described top-beaked cutting performance as the "feeling the chain is on backwards." This is the reason you should always try to get good corner alignment.
If you find that you need a "window" or some tolerance when aligning corners, set up your grinder (or file) so if you are going to be off some, you will never be high. If you end up on the low side, and your chain will cut great, it just won't hold the sharp edge as long as you'd like. Top beak it - and you will think you forgot to sharpen it.