This is a difficult question to answer in less than a day depending on whether you're referring to only the military structure (which recruited not only from a prince's most important nobles but also the towns, etc) or the economic structure as well but this isn't a terrible (and mercifully quick) summary I found with a few notes thrown in...
"Between 850 and 1200 the old tribal organization gave way to a stratified society. At the top stood the military caste, the druzhina, next came the merchants, followed by the artisans in the towns. These were all [truly] free men. The broad base was provided by the free peasants and hired workers. At the very bottom were the slaves - the institution of slavery was accepted by the Russians without question as was the case by most ancient societies. Although no opposing classes had yet [truly] appeared there was a definite division between the ruling, land-owning warriors and the laborers. It was the beginning of [an incomplete or undeveloped] feudal society.
Yet Kievan Russia was not essentially an absolute state. Democratic elements did exist. Meetings of tribal elders and of town folk (veche) originally administered and enforced the law. [note: the druzhina also often required consultation regarding 'policy' as well to retain their cooperation] The prince eventually superimposed his power over these primitive assemblies, except in Novgorod were the veche maintained its power for a long time until crushed by Muscovite absolutism."
edit: as an addition, while the land owning nobility did provide military service, the legal foundation of their property rights was hereditary, i.e. without obligaton of service to the prince. Later Ivan the Terrible (in the 16th C) I believe sought with the Oprichnina to create a purely service nobility to circumvent the traditional system, but most western feudal concepts become slippery at best in the Russian setting.