MagSafe is an Apple creation - their phones are equipped with a magnetic ring that allows the phone to attach magnetically to mag safe accessories - which maybe be anything from phone holders in the car, wireless battery packs, finger rings. It's very popular and if you put a case one an iPhone, many cases come with a MagSafe connector passthrough so you can continue to use the feature even with a case on. You can tell this with the recognizable ring with with the vertical bit at the bottom.
Samsung Galaxy phones do not have this magnetic ring of course, so many case manufacturers are now producing cases with this magenetic ring so that you can use many of the MagSafe compatible accessories that were originally intended for iPhones. I never used it, but a lot of forum members like it. I've so far do have some cases with it but I only use it for a magnetic finger ring so I can keep a good grip on the phone (don't like pop sockets).
It won't let you stick to a metal surface. The accessory will have the magnetic ring that will adhere to the ring in your case. While it also supports wireless charging accessories. It does not support any sort of data transfer. Most people use it for car mounts that have a MagSafe connector to hold your phone.