In this case "vertical integration" means that the rocket is standing upright while you are bolting the payload on to it. The alternative is "horizontal integr

In this case "vertical integration" means that the rocket is standing upright while you are bolting the payload on to it. The alternative is "horizontal integration" where you bolt the payload on the rocket while the rocket is laying on its side. You transport the rocket to the launch pad on it's side, and only there do you tip the rocket+payload together to be upright. This sounds like a very small detail, but many payloads turns out to be highly optimized to only receive forces in one direction, and their structure is not certified to be cantilevered in such a way to "hang" from the tip of the rocket body.