These days, professional video editing software often means one of Avid Media Composer, Adobe Premiere Pro or Apple Final Cut Pro. To the extent that it helps, we'll break the contenders down into categories. Which video editing software you ultimately choose is going to depend on a number of factors ranging from what capabilities you need to how much you are willing to spend.
So, you have a bunch of video and you want to edit it together into something that tells a story - you're going to need some video editing software.