If you have downloaded an MP4 file, but can't play it on your Mac with your regular player, it probably means that the player doesn't support the MP4 format. In order to play MP4 codec on Mac you can use one of the solutions described in this article.
Probably the best MP4 codec Mac player that supports this type of files out of the box. Elmedia Player supports a variety of codecs and doesn't require any additional installation of codec packs or any high maintenance.
Download MP4 codec Mac player and enjoy smooth playback without any breaks or slowdowns. Elmedia also supports multiple audio tracks, subtitles in different languages (external and internal), chapter points, bonus content, etc. Not only can this player display your videos in great quality, it can also fix possible issues with audio and video sync. It is a free MP4 codec Mac player, but also has a PRO version that can be purchased if needed and can stream MP4 files to Apple TV, take precise screenshots of any movie moments or convert the whole movie into the series of images that can be saved as TIFF, PNG, or GIF.
There is an MP4 codec download for Mac - Perian is a universal codec resource for Apple computers that is somewhat similar to K-Lite Codec Pack for Windows computers. Perian supports AVI, MP4, DIVX, FLV, MKV, GVI, VP6, and VFW file types and can be used with QuickTime Player, NicePlayer, QTAmateur and other QuickTime supporting players.
Note: Unfortunately the latest and last version of Perian 1.2.3 doesn't work with 10.8 (Mountain Lion), 10.9 (Mavericks), 10.10 (Yosemite), 10.11 El Capitan, 10.12 Sierra.
Another option to consider is converting MP4 files to a format that is supported by your current player. The Zamzar service is able to convert to many formats. You'll need to upload initial file to their website and enter your email address where you will receive the converted file. Such process definitely takes longer time than conversion with an app would.