That is a very broad question! :)

Politically, the year 800 was the birth of the Empire from what was a collection of "national" kingdoms collected under the reign of Charlemagne. The first Emperor died in 814, and by 817 his many descendants were already fighting for power. It was only in 843 that some stability happened when the nephews of Charlemagne divided the Empire in three parts, but again there were still rivalries and disputes between them and their descendants. This coupled with the threat of pagan peoples in the North (Normans), East (Slavs and Magyars) and South (Saracens). In 875 the main dynasty that ruled the central part of the Empire died off and civil war ensued. Eventually, a last scion of the Carolingians, Charles the Fat, united all the Empire under his rule just because everyone else was dead and had no legitimate sons. Charles was a weak ruler and he was dethroned by the bastard of his brother, Arnulf, in 887, dying the following year. What happened then is that, with no direct heirs of Charles around, anybody who could claim a link to the main family through female descendancy or illegitimate one, named himself king. By 889 there were 8-9 kings vying for power, and soon they also started claiming the imperial title. The Empire in 900 was nothing more than a memory, and the imperial title brought only prestige but no effective power.

Socially, though, something very important had happened in Europe. in 800 Charles' Empire was populated by Franks, Lombards, Bavarians, Alemannians, Saxons, etc. By the year 900, those distinctions had started to fade except that in legal systems, and most people were considering themselves Teutisci (Germans), Francisci (French) or Italici (Italians). The creations of a common Empire with common standards, the movement of people, mixed marriages and then the new division in kingdoms had almost erased the old nationalities and created new ones.

Again socially there was a large movement of people because of wars. In some areas the old aristocracy lost a lot of wealth and power and new men rose in their stead. In Italy, for example, all the main nobles were north Europeans because the kings would not trust Lombards, but then again by the end of the century many Lombards became prominent in the Church and were able to marry into Frankish or Burgundian families.

In many respects, the creation of the Empire brough people together by common writing (Carolingian minuscule), common weights, coinage, rules for the clerics and monks. Trade and travel were simplified. There was a resurgence of culture called the Carolingian renaissance with poetry, science and religious writings in which authors from France would discuss with authors in Italy, Germany, and even Spain or Britain.

So yeah, I would say that the 9th century was pretty crucial for European history!