The video implies that this is a specific video, whereas a video implies that it is only one of multiple videos.
For example, you watch a video about Calculus, but you would watch the video that was assigned for your math class.
With your example, it could go either way.
- I watched a wonderful video that explains Quantum Physics. Here is the link.
This works because there are many videos that try to explain Quantum Physics. So you use a.
- Here is a link to the wonderful video we talked about earlier.
You would use the here, because we are referring to a specific video.
In other words, you use the when there is no ambiguity. If you say the video, no one would question which video you are referring to (at least that's what the speaker is implying). A video is ambiguous and doesn't refer to a specific video, that is what your link is for.