After the Romanesque period in architecture, around 1100 AD, architects in western Europe gradually began to build Christian churches and palaces in the Gothic style. The easiest difference to see between the two styles is that while Romanesque churches have round arches, Gothic churches have pointed arches.
The idea for the pointed arch probably came from Islamic architecture, where slightly pointed arches appear as early as the 600s in the Dome of the Rock mosque in Jerusalem and soon became common in North Africa and Spain. From Spain, pointed arches arrived in Italy. Then architects began to use them in France and Germany, and finally in England.
But there are a lot of other differences between Romanesque and Gothic architecture as well. Gothic churches have many more windows, and much bigger windows, and so they are not dark like Romanesque churches. This is because the architects have learned some new ways of making roofs and of supporting walls. And, where many Romanesque churches had wooden roofs (which were always catching fire), Gothic churches had safer stone roofs.
Gothic churches in northern Europe are also usually bigger than Romanesque churches there. By 1200 AD, people in northern Europe had more money available, and they could afford to spend more on building great churches. They had conquered a lot of southern France, and they were trading more with the Islamic Empire.