This style of roof is named after a 17th-century French architect Francois Mansart (1598-1666) who used this design of roof on many of his buildings. A mansard roof has the advantage of maximising the available space within your loft.
Mansards are commonly built by raising the party/gable walls either side of your house to make the profile for the mansard and then creating the timber frame. Although common on older properties, especially in cities like London, Mansards are not often seen in the suburbs. Flat roof dormers tend to be a more popular choice for the 'average' 3 bed semi or terrace house due to the reduced cost and simpler construction. A mansard loft conversion will almost certainly require planning permission. Things to consider.
While this type of roof will give you the maximum amount of space in your loft conversion it does a downside. As it involves replacing the entire roof the constructions costs will be high. Therefore, it is quite unusual to see this type of conversion, unless the orignal roof was built in this style.