MKV file extension is a Matroska Video file. The Matroska Multimedia Container is a free and open container format, a file format that can hold an unlimited number of video, audio, picture, or subtitle tracks in one file. It is a universal format for storing common multimedia content, like movies or TV shows.
Matroska is similar in concept to other containers like AVI, MP4, or Advanced Systems Format (ASF), but is entirely open in specification, with implementations consisting mostly of open source software. On Android devices you can open MKV file extention using Playit app, and for Iphone iOS you can download VLC app from App store.
Your best bet for playing most MKV files is to use VLC. If you're on Windows, some other MKV players include MPV, MPC-HC, KMPlayer, DivX Player, MKV File Player, or The Core Media Player. Some of those applications will open an MKV file on macOS, too, as can Elmedia Player. Although it isn't free, Roxio software can be used to play MKV files on macOS as well. On Linux, open MKV files using xine and some of the programs above that work with Windows and Mac, like VLC.