As far as the High Middle Ages are concerned, many of its most important cultural and intellectual achievements were closely intertwined with the church. Indeed, it was in the High Middle Ages that the university system had its origins, with some of the world's oldest universities (including Oxford, Cambridge, the University of Paris, and the University of Bologna) having their origins in this time period. In addition, there was the further maturation of scholasticism, represented in the work of such important thinkers and theologians as St. Anselm of Canterbury, Peter Abelard, and Albertus Magnus, to name a few. This was also a time period quite important to the future development of science, given that it saw with it a revived interest and veneration of Aristotle and thus did much to help establish the reputation of empiricism within European intellectual circles.
In addition, the High Middle Ages was also an era that saw tremendous architectural achievements, particularly reflected in the construction of cathedrals. Two of the most famous masterworks originating in the High Middle Ages were the cathedral at Santiago de Compostela in Spain and Notre Dame in Paris.
If you were to look beyond the realm of the church (one of the critical pillars of medieval civilization), you would observe that the High Middle Ages was also a period of population growth, where cities were growing and trade was reviving. In many respects, then, this can be viewed as a critically important turning point in the history of Europe.