In brief, Alexander I of Russia joined an alliance with Napoleón I after a Russian army was routed at Friedland and Prussia was decimated at Jena-Auerstedt. This was a mutually beneficial arrangement in many ways (unlike the humiliating terms imposed on Prussia), but part of the agreement was that Russia would adhere to the Continental System -- a French initiative which involved all French allies and satellite states not trading with the UK in order to erode their ability to continue funding a war effort.

Participation in this embargo was an economically onerous burden for Russia. There were also other incidents, such as the Russian court maneuvering against Napoleón's attempts to marry the tsar's sister, France's peeling off of Galicia from Austria and granting it to Poland rather than Russia, and Foreign Minister Talleyrand essentially working against Napoleón in the tsar's court after having decided that the emperor whose 1799 coup and 1804 coronation he'd previously supported no longer represented the best interests of France.

So, after three years of halfhearted participation, Russia withdrew from the Continental System in 1810, thereby weakening Napoleón's geopolitical position and Alexander began warming himself back up to Russia's old British allies (with whom he had technically been at war since 1807). Two years later, he demanded that French troops evacuate Poland and Prussia, to which Napoleón--not really left with much of a choice--responded by declaring war on Russia.