The codec is the one that the video has been encoded with. Some many video players require that you have the necessary codecs installed. VLC is one of the exceptions and has its own codecs for the most commonly used formats.
Another way of checking how a video is encoded is to use MediaInfoOnline - MediaInfo in your browser. Nothing is uploaded anywhere so don’t worry about file sizes and bandwidth.
The following is a codec pack that many refer to when people are having trouble playing videos: Download K-Lite Codec Pack Mega
I usually download the basic version instead of the mega version since I don’t want to pollute my computer with too much irrelevant stuff: Download K-Lite Codec Pack Basic
You can compare different alternatives here: Download K-Lite Codec Pack
Note that this is not the only codec pack available, it’s just a popular one.
There is a thread about codecs and applications that might (or might not) help: Codec Support with Programs