These castles are called "motte and bailey" after the peculiarity of their design. The major strongpoint, the keep, was built on the top of a flat-topped conical mound, the "motte", surrounded by a ditch and embankment, with an area of ground attached, also protected by at least one ditch and bank, the "bailey". Whilst the ditches and banks were man-made, the motte could either be man-made, or a suitably sited natural feature. The banks would have been topped with palisades or walls, with the usual complement of towers and gates. The bailey provided a secure site for the ancillary domestic buildings such as hall, chapel, stables etc.
It may be incorrect to say that this style of castle design was only introduced into England with the Norman Conquest of 1066. England was not so isolated either politically or culturally from the mainland of Europe that such things were completely unheard of. My references point to a few sites which are clearly stated to be 'pre-Conquest'. What is most certainly true is that the Conquest brought about a massive increase in the number of such castles.
Most of these were built as a temporary means of subduing a nation which would not take kindly to Duke William of Normandy forcefully making good his claim to the English throne. To this end, William shipped large numbers of castles from Normandy to England as wooden prefabricated kits of parts. Once the earthworks had been constructed, these temporary wooden keeps were erected on their mounds and served a similar purpose to the turf-built forts of the earlier Roman occupation.
In due course these castles were no longer needed and were dismantled, leaving only the earthworks behind. Many towns and villages which existed at the time still display the physical remains of these structures. There were, however, a number of sites of particular strategic importance, and it is certain that the castles built there were designed to be permanent fixtures. That is, they were built in masonry from the beginning.
Whilst there were no great engineering problems concerned with building stone walls and towers on the tops of the embankments, the same was not necessarily true when it came to building the stone keep on the motte. If the motte was a natural feature, then the ground may have been compact enough to take the force of many tons of stone resting on it. If the motte was man-made, then any stone keep built on top of it would have collapsed in short order.
To overcome this problem, the castle builders adopted two solutions. The first was to minimise the amount of masonry by building a "shell-keep". This was basically a simple circular wall enclosing the top of the motte. The accommodation was formed by building lighter structures against the inner face of this wall, leaving an open courtyard in the middle. This alone would not have completely avoided the problem of subsidence, and there is archaeological evidence to show that the foundations of the shell-keep could be at the natural ground level and the wall and mound raised together, effectively giving a very tall masonry structure with most of its bulk buried within the mound.
Although my illustration shows the classic "motte and one bailey" design, this was by no means the only form. Many castles had two or even three baileys. In the case of a castle with two baileys, the military thinking of the time often resulted in the "hour-glass" design, the two baileys being arranged either side of the motte.
Two examples of this are Arundel Castle in Sussex, and Windsor Castle in Berkshire. Whilst both castles are today what I would classify as "Stately Homes", having been quite extensively rebuilt and modernised, their distinctive plans show quite clearly their ancient origins.