This is usually requested by many journals nowadays. In case a paper has been submitted to journal A, got rejected and the authors chose not to change the paper or fix it. Then, theses authors submit the same manuscript to a different journal for possible publication. This paper would have to go over the same review process (although maybe with different reviewers), this would waste time and effort and in a way not fair (to other manuscripts) since this manuscript got rejected for not having correct/solid results (for instance). Since this paper has been reviewed by 2-3 experts in that particular field, it is best to address any issues raised to arrive at a higher quality paper.
In another scenario, the reviewers might request the authors to add additional analysis, literature review and/or redo an experimental testing (or even add some), then the authors chose not to change the paper and decide to try their "luck" and submit such paper to another journal. Again, this paper would go through another round of review that could result in raising the same issues(or even different issues) compared to that of raised by reviewers of journal A.
Since editor of journal A does not have access to editor of journal B and reviewers can review papers from multiple journals, there is a chance that the manuscript would be sent to one of the original reviewers! Or even getting different or similar comments to that of the first review. In this case, this paper has been circulating around for two rounds of review (maybe for 4-6 months)! and did not improve academically/scientifically.
Simply put, papers are meant to be published if they are of quality, merit and with minimum "issues", not for the sake of publishing! Hence the role of reviewers and peer review process. Remember no one can have a perfect paper, which is fine, but having a paper with questionable results or were flags are raised and have not been addressed is not acceptable!
One more thing, if I'm not mistaken, I believe some journals now request reviewers to re-review the manuscript if it was rejected and re-submitted to a different journal. Maybe somebody can confirm this as I have heard it from a colleague.