Failure of an earlier glue joint. You will have to dig out the old glue, which will leave gaps, so this is a job for Acraglas or a high quality slow-set epoxy and, likely, floc. Focus should be on maintaining a nice tight wood-to-wood fit at the surface. As others have said, blind pins would reinforce the joint. I prefer threaded rod. Since both sides are broken away, you should be able to glue one side and then drill for and install the pins from the other side. The pin holes for the opposite side will have to be done blind. My method is to drill the holes to a specific depth on one side of the break. Make a pin with one sharp end that is about 1/16" longer than the hole depth. One-by-one, drop the pin in the holes and press the pieces together. The sharpened pin will mark the locations of the mating holes. Has worked for me many times. A coat of paste wax on the wood surfaces should keep any squeeze-out from sticking. As an alternative, masking tape can be used in the non checkered areas.
Those appear to be clean breaks, so repair should be pretty straightforward.