What effect did the Roman Catholic church have on the architecture of the middle ages?

The medieval period saw an enormous rise in power and wealth for the Catholic Church.  This was a time in which the people tithed 1/10th of their earnings to the church along with other payments for services like baptism, marriage, communion, etc.  Criminal law was also attached to the church which allowed the church to exact penance.  The wealthy often donated land to the church for the construction of churches and monasteries.  Due to the influx of money and land, the Catholic Church was able to build many churches during this period.  The largest churches were called cathedrals and they marked the landscape over all else in medieval cities.  Since they were built to inspire awe – they were often very tall, imposing structures that would make an impression on all inhabitants.  They were among the most expensive and lavish buildings built at the time, some taking hundreds of years to complete. 
During the 12th century there was a new and very popular architectural style developed after the rise of the Romanesque style – the Gothic style.  Gothic architecture fulfilled the desire for soaring heights with the use of a rib vault, flying buttress, and pointed (Gothic) arch.  These high walls also included plenty of space for windows to allow for a well-lit space.  Stained glass windows were used for a dual purpose – to communicate stories from the Bible to the mostly illiterate public, and to create an almost mystical, magical effect which would heighten the experience of the church goer. 
Since there were so many architectural innovations which came from the creation and design of the Gothic Cathedrals, those same techniques and esthetics were carried over into other buildings such as civic buildings, universities, castles, and town halls.  The same goal that the church had, to draw the eye and inspire awe, was used by those building the institutions of a town or region.   Architects and builders discovered that using pointed arches allowed for much greater strength and stability, thus allowing them to build taller buildings with thinner walls than previously used.  Those thinner walls allowed for more window openings as well.  Decorative elements like gargoyles became popular on the tops of Cathedrals and some other buildings; allowing for water to be washed down the side of the building instead of leaking through the walls.  Even though this style of architecture became popular and used in all types of buildings, even today the most famous examples (and amongst the best preserved) are the great cathedrals of Europe, still leaving their mark hundreds of years later.
 
https://www.britannica.com/art/Gothic-architecture