Modified from an earlier answer

In early modern studies, it is something of a cliche to describe the HRE as a peculiar institution, but the description is somewhat apt, especially prior to its dissolution in 1806. The Reich was not, and never really was, a unitary state, but rather something approaching a confederation of multiple polities ranging from free cities to principates and bishroprics. Voltaire's famous quip that it was "neither holy, nor Roman, nor an empire," while catchy, obscures analysis of the HRE because its political culture and Reich structures had really abandoned these ideas or interpreted them in a way that cannot be reduced down to their fundamental definition. For example, the Peace of Westphalia had cemented the idea that confessional choices fell under the purview the local states' rulers (cuius regio, eius religio) which led to a great seal of state sponsorship of theology and forms of religious expression. Whether in the Pietist theology produced in University of Halle or the various Catholic ecclesiastical music produced in the Archbishopric of Salzburg, the HRE was arguably at the forefront in European Christian thought and expression in the eighteenth century, so in that sense, it was rather "holy," at least compared to its contemporaries.

As for how the HRE functioned in the eighteenth century, the basics are as follows. All of the multiple polities within the HRE enjoyed their own degree of sovereignty, but were also subordinate to a variety of imperial institutions and responsibilities. During the eighteenth century, the three main HRE institutions that were most salient in the lives of Central Europeans were the Reichstag (imperial diet), the imperial Kreise (circles), and the various forms of imperial law.

The Reichstag met permanently in the city of Regensberg from 20 January 1663 to the dissolution of the HRE. The Reichstag itself covered a bewildering array of functions, ranging from legislation of laws, the approval of levying imperial taxes, or maintaining contact between the emperor and his many subjects. The last function was actually quite critical because the Reichstag was not so much a conventional diet that represented the common people of the HRE, but instead was a institution meant to represent the various rulers and polities of the HRE. The Reichstag existed as a conduit between imperial power and its various components. The perpetual Reichstag allowed for some degree of collective action and coordination for such a polyglot territory. Various factions and alliances within the institution emerged that made it easier for smaller polities to air their grievances and desires. Although the system was very incoherent and as a parliamentary body the Reichstag was comparatively weak, it was not a toothless echo chamber. For example, when the French Revolutionary governments abolished feudalism in Alsace in 1789, the Reichstag declared the action illegal in 1791, but left it up to the emperor to either negotiate with the French or declare war.

While the Reichstag was a conduit between the emperor and its components, the imperial Kreise were geographic divisions of the empire intended to provide a collective defense of the HRE. The Kreise encouraged regional economic development and the Reichstag delegated control over the currency issue to the Kreise. This system of collective defense worked moderately well in the late seventeenth century, especially in wars against the Ottomans, but was increasingly difficult to manage as military establishments increased in size and cost during the eighteenth century. Larger states like Bavaria began to dominate their respective circles and the advent of Prussia destabilized this dynamic even further. But in theory, the Reichstag had the potential to raise a Central European Reichsarmee , and existence of the Kreise would make such a military formation a more tenable proposition. Many of the small and middling HRE states saw the Kreise as a vital component for their security as its existence precluded them from being swallowed up by their larger neighbors.

The most potent and active symbol of the Reich's governmental organizations prior to dissolution was its legal system. The HRE maintained two imperial supreme courts, the Reichshofrat (RHR) and the Reichskammergericht (RKG), and a network of lower-level territorial courts, Hofgerichte. This web of imperial laws coexisted with local legal establishments and imperial law often served as a mechanism for appealing decisions reached in the local courts. In an age of absolutism, HRE territorial rulers had to walk a fine line in trying muzzle or control local courts as the imperial appeal mechanism remained intact. Although a number of the larger principalities had sidelined the imperial court system by the late eighteenth century, they often did so not by ignoring the imperial courts, but by streamlining and rationalizing local courts so they were a more attractive venue to settle legal disputes. The imperial court system also provided a venue for smaller polities to have a voice beyond the Kreise or Reichstag. The potential of the imperial courts system was illustrated in 1802 when Württemberg, Bavaria, and Kassel used the disorder created by the French wars to occupy land controlled by the Imperial Knights. A flurry of appeals to the RHR led the emperor to order the return of all occupied territories in 1804 as part of a wider defense of the imperial constitution.

Executive authority within the HRE is a tricky issue and one that is difficult to parse out. By the eighteenth century, the Habsburg emperor was nominally the head of a grouping of equals and was supposed to coordinate the various Kreise in time of crisis after having received sanction and support from the Reichstag. However, the polyglot nature of the HRE made this increasingly harder to coordinate imperial interests with local ones. In the case of external threats, like the Ottomans, the system of delegated authority worked reasonably well, but other European crises less so. The advent of Prussia's Machtstaat upset this balance even further as one of HRE core constituent members now had the ability to strike out in its own interests and pursue its own policy of territorial aggrandizement. Using its own army as leverage, Prussia was able to either pursue a foreign policy independent of the HRE
as it did during the Silesian Wars, or pose as the Reich's protector against Habsburg aggrandizement as it did during the War of Bavarian Succession. Although Prussia's relative autonomy in the Reich meant it could be flexible in its approach to imperial politics, the fact that it was the least of the great powers coupled with the fact Prussia's strength alienated it from Austria, meant that Prussia often had to rely upon external allies like Russia, which allowed for foreign penetration into the HRE.

Therefore the Austro-Prussian rapprochement of the early 1790s sent shockwaves through many of the systems and political of the HRE. The fear was that united together, these two states would carve up smaller territories and run roughshod over imperial institutions of collective security. The actions of the Revolutionary government in Paris in seizing territory of the Rhineland in violation of existing treaties provided something of a pretext for the smaller HRE territories to demand that the emperor honor imperial security. Both its geographic proximity to France and the domestic autonomy of its rulers meant that the ecclesiastical principalities often became a haven for French emigres as the Revolution became more violent. The French declaration of war on Austria prompted prompted the Austrians to act in order to keep the delicate Austro-Prussian rapprochement intact by planning to divide Rhineland territories. The Reichstag itself waffled on supporting this effort,, with Hanover resisting attempts to raise subsidies for the war effort and many of the smaller states correctly seeing Austro-Prussian success as being to their detriment. Although the Reichstag did concede that the French had declared war on the HRE and declared the war a Reichskrieg in 1793, its funding and support was often tardy and conditional. This meant that the burden of fighting the French largely fell on Austrian and Prussian shoulders in theaters quite distant from either Berlin or Vienna, where fighting the French war, which was never that popular to begin with, became increasingly an undesirable situation. Prussia's separate Peace of Basel was the culmination of this distaste for intervention. This created a dangerous precedent for the Reich as various territories like Baden and Württemberg were able to conclude their own individual armistices with the French in 1796.

Could you be a little more specific? Do you want to know about the imperial administration? Territorial gains? the Centralisation of the empire? At the time of the French Revoultion, the title of "Emperor" had become more of a hereditary honourific title passed down by the Hapsburg Dynasty.