Well, there are several ways to play such a file. First we will enlighten you with an explanation what "mkv" stands for:

"The Matroska Multimedia Container is an open standard free container format, a file format that can hold an unlimited number of video, audio, picture or subtitle tracks inside a single file.[1] It is intended to serve as a universal format for storing common multimedia content, like movies or TV shows. Matroska is similar in conception to other containers like AVI, MP4 or ASF, but is entirely open in specification, with implementations consisting mostly of open source software. Matroska file types are .MKV for video (with subtitles and audio), .MKA for audio-only files and .MKS for subtitles only. The most common use of .MKV files is to store HD video files...."

More on Wikipedia.

So, how you are going to play this nice video file? As we told you, there are many tools out there to play this but we recommend to use the VLC media player, or just in short VLC from videolan.org. (You will be able to find the proper download link on there site)

About VideoLAN

VideoLAN is a project, run by volunteers, backed-up by a non-profit organization, which produces free and open source software for multimedia, released under the GNU General Public License. The main software is the cross-platform VLC media player.

About VLC

VLC media player is a highly portable multimedia player supporting most audio and video formats (H.264, Ogg, DivX, MKV, TS, MPEG-2, mp3, MPEG-4, aac, ...) from files, physical media (DVDs, VCD, Audio-CD), TV capture cards and many network streaming protocols. It can also convert files, transcode and act as a streaming server over unicast or multicast and IPv4 or IPv6. It doesn't need any external codec, program or codec pack to work.