Minimalist shoes are designed to mimic running barefoot which encourages a more natural running motion. This way of running, if done correctly, is believed to strengthen your feet and lower leg muscles while reducing the risk of injuries. It is important to realise that in order to run in these shoes you have to run with a midfoot to forefoot strike. This allows for your calves to help with shock absorption rather than sending it all up through the joints. There is more to the technique of minimal running that just where your foot strikes so it is important to read up on the subject and start off small.
Minimal shoes will vary in the amount of protection that they offer, from practically nothing to what can be considered a transitional shoe. What all minimal shoes share is a reduction in heel drop, so the height between the heel and the toes. Regular road shoes will offer between 10-14mm more bulk at the heel, due to the shoes being designed to deal with landing on the heel. A minimal shoe generally offer zero drop (completely flat) up to around 8mm. The reduction in bulk at the heel is because the cushioning is not needed there when striking mid/forefoot. It helps to reduce the weight of the shoe and to land more efficiently.
PLEASE NOTE: It is important to ease into barefoot/minimal running gradually to reduce the risk of injury. Many Brands recommend using a minimal shoe for no more than 10% of weekly mileage to begin with to allow the runner to get used to running more barefoot.