I've seen some posts floating around about what a distributed version control system might give you. For me, these are the key elements:
Committing changes is separate from sharing. While the phrase "you can edit on a plane!" gets thrown around quite frequently, I think this is the far more important aspect of that vision. As a developer, you don't always know how a particular path of development might impact the code base. With a purely centralized system, you have to think first about where a path may be taking you as it could affect everybody else. Time and time again, I've seen developers work without any revision control safety net for days or weeks at a time because they don't want to "break the build", and they don't have time to look up the policies for branch naming, merging, etc. Not that such a thing should take a long time, but when under pressure, it's the last thing one wants to deal with. And the untracked changes keep getting bigger, and bigger. And when I say "I've seen developers..." here, I include myself.
With a DVCS, I can commit immediately. I took heavy advantage of this on a recent project where the set of work for which I was responsible was in no state to be set up on other systems. It required new configuration and possibly new tool installations and I didn't have time to help everyone else install and update their sandboxes. They didn't need my code anyways. Instead, I was able to pull in and rebase my work on updates from my co-workers while my personal branch was in development. When my code was mature, it was easy to merge into a more centralized branch. Very easy. In fact, it was just a fast-forward (in Git parlance), since I was rebasing my changes on top of those by my colleagues.
Again, this is possible with a purely centralized system, but it would have required me to realize the significance of my changes and their impact on others. My sandbox was in a "guts on the table" kind of state. Just about every commit I made was stable, but sharing them would have made it harder on other team members to do their work due to the changes made in tool and configuration dependencies.
In essence, a DVCS inverts the control back to individuals. As a developer, I can commit my changes whenever I want. With a purely centralized system, I have to think more about what I'm about to commit, since it immediately impacts all other developers.
A DVCS encourages experimentation. Being able to commit my changes whenever I want and being able to make local branches so easily makes it easier for me to start playing around with new ideas. Whether that's doing a big refactoring or restructuring of code, experimenting with a new feature of third party library, or working on updating the code to run well on the latest release of Foo, I know that I can experiment and SAVE those experiments in small chunks, without impacting anybody else. I can choose when and how I want to share my results. I can choose to throw my experiment away and not have to be reminded by its grizzly branch name for years to come.
We have an internal toolkit that bridges SQLAlchemy and Zope 3 and provides various other useful features and integrations. Late last year, I started looking into updating the code to work with SQLAlchemy 0.4 and to also clean up some ancient hacks. We were still using CVS at the time. I can't remember when I made the branch, but I knew at some point that I was heading down a potentially long path and that a branch would be required. Other priorities were coming up and I'd have to leave this work aside for a while.
Well, there's 2-3 days of feverish work, all held hostage within a single check-in. I've been wanting to pull some features out of that branch and into the current mainline branch, but since it's all in one big check-in, I can't do that easily. This is the second time I've done that (the other time was on a feature branch that lead to a dead end, but along the way I had some good ideas that I'd love to be able to extract now).
If I'd been using Git, I would have been making more commits, more frequently, and in much smaller sizes. Using Git, I would then be able to quite easily cherry pick individual commits out of that branch and apply them to the mainline.
Finally, a DVCS makes it easy to vet changes through the system. We don't have to give new employees the keys to the kingdom, particularly when their skill set is focused on a specific area. Instead, the code can go through review channels. They make commits in their local repository, and tell someone (like me) that they've made some changes. Using Git (or any other tool - but Git's named remotes makes this hella easy), I can pull in changes from their repository, verify that they're good, and push them to the canonical repository. I can merge them into other branches, if required.
Imagine this in a team situation: team members can share their repositories with each other as needed, giving each other chances to do code reviews and fixes before sharing those changes with the larger group or division; all without requiring permission to touch the central repository. Suddenly whole new workflows open up, based on the "networks of trust" inherent in all of us: a team leader collects commits from their team, and shares those changes with other team leaders. Those team leaders pull together changes from all of their teams (while sharing said changes across team lines) and push those on to a QA / Testing division. The QA / Testing division then puts their seal of approval on things by being the ones who control pushing to the "canonical" repository from which builds are based.
There's just so much more that can be done with a DVCS, and we're in an age now where there are very usable and useful tools for this job. A DVCS restores individual responsibility, encourages experimentation, enables adaptive workflows, and I believe it fits more naturally into how we humans organize our interactions. Whether this is in a rigidly defined corporate structure or a loosely connected set of worldwide open source contributors, the peer to peer nature combined with getting the whole repository enables people to step up and do bold things without having to go through channels to get any coveted "write access".