As has been said, Google SERP's often change like this. Some terms sometimes are dramatic, while some terms sometimes are not dramatic.
Not sure how you are checking your backlinks, but Google will only show a sample of links by design.
All-in-all, what you describe doesn't sound that dramatic. But probably is to those effected. Many of our pages moved up the SERP's last week (some also fell but a lot less). This was do a jig time for us and "dramatic", but for the rest of the world it's just another day
Keep in mind that, for every page that falls another rises and vice versa.