A planned town is one that has been designed from the beginning, rather than one that has grown up gradually over the ages.
People have planned towns since earliest times. The Sumerians of the Middle East planned the first city in the world. It was called Ur. The Ancient Egyptians built new planned cities. King Akhenaten (Tutankhamun's father) built a new city called Armana in the deserts of Egypt as his new capital.
When people plan a town, they often do it using some kind of pattern. That is they use shapes like circles and stars. They are using what we call geometry. The simplest kind of plan is to make a crisscross of streets that cross each other at right angles. Many American cities were planned this way. People in the Muslim world preferred circles. Ancient Baghdad was built on that pattern.
Many capital cities are planned cities. Washington DC is the planned capital of the USA; Ottawa is the planned capital of Canada; Canberra is the planned capital of Australia. Sometimes these planned cites have been placed far from existing cities. The world's most dramatic example is Brasilia, the planned capital of Brazil, built hundreds of miles from any of the existing cities.
More recently, people have tried to build with many open spaces. In the 1920s, a number of towns were built to look as though they were actually in the countryside, with wide tree-line streets and open spaces. These were called Garden Cities. The most famous of these is Welwyn Garden City in England.
The New Towns built after the Second World War in Britain were built because of the war damage. That is what makes them unique in the world. Planners saw that they could not rebuild the bombed cities fast enough, so they started to build new towns in the countryside away from the cities. People then moved into these towns, giving a chance to rebuild the old cities over a longer time.