This is "tearing" of the video.
It's actually quite well document on this site.
Here's some links for you, for further reading:
It's an issue with the signal, in conjunction with the recording VCR (and sometimes even the playback VCR, although not as common).
The links above explain it in quite a bit of detail, from the technical reasonings, down to the available fixes. Assuming these are not copies of copies of copies, the error is generally quite correctable.
Note that it does require more video hardware. Should you find the chore of buying/learning/using more video hardware undesirable, remember that The Digital FAQ also has video conversion and restoration services. Just wanted to mention that.