I decided to make the change to reduce the long-term wear and tear on my joints (particularly knees & hips). I like the way I feel running barefoot-style with a midfoot landing.
I found it useful to use minimalist shoes (Terra Plana Neos in my case) because you get more feedback from the ground (and if you stop thinking about what you're doing and drift back to heel striking, your heels tell you so PDQ).
It IS about changing your running style - shorter strides, landing with your foot under you rather than out in front, faster cadence (180 steps/minute, or so) - not just which part of the foot you land on.
Note, it does put more stain on your achilles tendon and calf muscles, also, going minimalist increases strain on foot tendons etc., so it's advisable to strengthen those (see info on barefoot running forums). Maybe start with short runs in minimalist shoes (cheap starter option is water shoes, £3.99 from Lidl last week, or use a pair of racing flats if you've got them) for improved biomechanical feedback, while doing longer runs in the more padded shoes you're used to. Also, drop the mileage right down to start with - you'll really feel it in your calves initially. Not sure about changing gradually - might be confusing; other people may be able to advise you on that.
Note that purists will say run barefoot to improve your running form. May be true, but personally I like the protection from dog poop, glass, thorns etc. hidden in the grass!