The media player on your device may not succeed at opening video files with an MKV extension because it lacks the necessary codecs for decoding this file type. Codecs are a viable option because they give your media player the ability to decompress and play the MKV files it does not natively support.
It is a great way to easily turn any media player into an MKV file player, but can also be dangerous to your computer. You need to ensure you download codecs, or any other necessary software, from recommended sites. Some sites hide crapware in popular software; thus, putting the security of your system at risk.
If you are unsure where to start, head to Niite, a great place for lots of clean and useful apps for your device. This site provides free downloads devoid of any bloatware. Once at Niite, search for a codec pack named Combined Community Codec Pack (CCCP) which offers a variety of codecs that support multiple file formats.
On the Niite landing page, select the CCCP option and click "Get Your Niite". The file will begin to download, and once finished, run to install the codecs. While at it, you may choose other apps you may fancy from the site, and install them as well. To effect the changes, you may have to restart your computer, though in most cases, your MKV files should start playing promptly.