Peter the Great's lasting legacy came out of his policies of westernization. When he was still young, he actually traveled throughout Western Europe, and when he returned back to Russia, he implemented reforms based on what he observed. These would have lasting effects in shaping the the Russian Empire for generations to follow.
Peter the Great created the first modern standing army in Russian history (inspired by what he observed from the military reforms in the West). He implemented military drafts to create an infantry, hired Western military experts to train his soldiers, and invested in Western-style armaments to equip them. At the same time, he also invested in a navy. Under Peter the Great, Russia's military power expanded dramatically.
In addition to military reforms, there were also administrative reforms under Peter the Great: he created new forms of taxation as well as state monopolies to increase state finances. He also instituted the Table of Ranks, which tied the Nobility to the interests through the states because it
required all male nobles to enter state service and serve in the army, navy, or bureaucracy, and allowed commoners who rose through the bureaucracy or military to assume noble titles."(Merriman, 274)
In short, Peter the Great had a profound influence on Russian political and social culture, overseeing a policy of extensive westernization. In doing so, he dramatically increased his country's military power and did much the same for the political power of the Russian state.
Citation Note: In answering this question, I drew heavily on the following source for information on the various reforms carried out under Peter the Great: John Merriman, A History of Modern Europe: From the Renaissance to the Present (Third Edition). New York: W. W. Norton, 2010. (271-277).