What reaction occurs when soaking a piece of meat in apple cider vinegar?
This "cooking" phenomenon happens because of the basic building blocks of a meat (protein) and how they can be broken down (which is called "denaturation"): heat (traditional cooking), pH changes (your vinegar question) or enzymes (bromelin or papain, which are typical ingredients of meat tenderizer)

When exposed to these factors, the proteins that make the bulk of the meat "break", and the result you can observe is very similar, which is the "cooking". Since it varies with the exposure level to the denaturating agent, this is why you only see the "cooking" happening on the surface of marinaded meats. 

pH changes is also an alternative "cooking" method used in some dishes, e.g. ceviche, which is raw fish finely chopped that is soaked in lemon juice to "cook"

Hope it helped :)