The apple pictured is a of the Gala variety,typically striped.The stripes swirl around a brown protrusion. The protrusion is flexible,in the way a leaf is flexible. The flesh underneath is not discolored or soft. The apple is not misshapen,the seeds are not un-developed or underdeveloped. What is this brown protrusion called and what causes it?
I take it that the question is about the mis-shapenness of the apple, that the stick we see in the dip is the core. The morphology (shape) of fruits such as apple and pear are very sensitive to how well the fruit was pollinated. As we know there can be a variable number of seeds in an apple, but the important fact determining shape is that there should be viable seed develop in each of the five seed pockets resulting in balanced development of the fruit. If the pollination is poor and only a few embryo seeds are fertilized, then the development of the surrounding flesh will favour the pockets that contain viable seed, resulting in possibly mis-shapen fruit. Once you have wondered enough and decide to eat, cut open carefully and on the small side you should see that the seeds are either too few, non-existent or failed to develop.