Scrum has three phases. First is a planning meeting where you decide what you will do over the course of the iteration. Next are brief daily stand ups where you describe what you did yesterday, what you are doing today, and any blockers. And finally there's a retrospective where you review what you did over the iteration to understand what went right, what went wrong, what you can do to improve the process.
I find Scrum to be a lot more enjoyable than most team-organizing processes. The planning meeting is about the same as most planning meetings. Nothing new there. It's the stand ups and the retrospectives that make Scrum pretty neat. The stand ups are brief. All too often people turn daily meetings into chat sessions. I hate those. Instead with Scrum the idea is to give the team (and especially the product owner / project manager) an idea of where you are at. An astute product manager uses that for course correction if need be. And it also gives you a chance to setup a side meeting if you need to collaborate with someone. The retrospectives are where you'll find team building. When things go right, you want to celebrate those. When things go wrong, you want to learn from those. When someone has an idea about how to improve the process, they get a chance to bring that up so that things can improve and they can get stuff off their chest.
So Scrum maps well onto three things groups need to do: plan, give status, and review/improve. And like any process, someone could become fanatical about it (which I think is a loss, and counter to the flexibility the scrum.org coaches recommend), but it's a nice jumping off point for creating a process that works for your organization.
BTW: there's more to Scrum than that, like the whole pigs vs. chickens things. I don't find that very useful. Scrum also leans away from a project-manager/leader kind of organization. To me that's like having an orchestra without a conductor, so I don't find that useful either. But parts of Scrum I find very useful indeed.