In many ways Gothic arches are a natural evolution of the preceding Roman and Romanesque rounded arches. The change came as a by-product of architects' constant attempts to build higher and allow in more light. For centuries arches were topped by the high point of the round shape, but by bringing the top of the arch to a point, architects could have their arches reach higher, giving their entrances and windows greater height and more room to let in light.
Gothic arches afforded architects of two advantages, the first being the obvious one of greater height from a given width. The second advantage was in weight distribution around the arch. Given the amount of pressure the stone walls place around the arch, masons of the time had to be considerate of not only vertical forces but also of the side displacement that most arches cause. While stone walls can tolerate a great deal of downward force, too much weight distribution to the sides causes them to topple over. By pointing the top of the arch instead of rounding it, Gothic architecture allows the arch to absorb more of the vertical pressure while displacing less toward the sides. The greater weight absorbed by the arch meant the surrounding walls themselves could be thinner.
Gothic windows, which used pointed arches, often included internal tracery, which also used pointed arches. Typically the arches within the tracery are thinner than that of the entire window. The tracery cast a dramatic shadow when light came through; served as decorations within the window, which allowed each building to have its own distinct window design; and served to support the window itself by allowing a little bit of its weight to come through the tracery, which in turn allowed the windows to be higher and wider.
The use of pointed arches is also commonly employed on the interior of Gothic buildings, with hallways and large chambers using the same shape to allow for wider openings. Further arches in the form of columns and external supports called flying buttresses absorbed the weight of the ceiling. By using the arches, columns and buttresses to distribute the weight downward instead of outward, the walls of Gothic buildings could be thinner, presenting greater opportunity to install windows and openings.