Shamelessly copied and pasted from Reddit:
The situation from Russia's perspective:
Primarily Russia is securing the future of the Black Sea Fleet, in case the Ukrainian hardline Nationalists decide to break the treaty and take the Russian naval bases in Crimea. Base reinforcement was a preventative measure to nip any such action in the bud. Had Putin not done so and if the new Ukrainian government was foolish enough to take it by force (as some were suggesting) then there would have been an unavoidable war. Russia NEEDS warm water ports in Europe, this has been the the historical catalyst for over a dozen wars for Russia, under no circumstances will they give up their naval bases in Crimea. A show of strength is intended to show their commitment to keeping those bases. That is the bottom line of this situation, the ports must stay at all costs.
Naturally Russia is not happy with the turnout of the Ukrainian revolution. The way it sees it, a violent nationalist opposition overthrew the pro-Russian majority elected President of their close neighbor and ally. As a result a significant (ethnically and politically Russian) segment of the Ukrainian population now finds itself without due representation in government. In response Crimea, a historically and ethnically Russian region, declared autonomy from the "usurper" government in Kiev. A new government that through both action and rhetoric has shown that it is both volatile and not opposed to using violence to silence its pro-Russian opposition, something that they themselves condemned when it suited them. The Crimean administration has requested Russian troops stationed in Ukraine for protection from an otherwise likely attempts by the Kiev government to violently put down the Crimean revolt until the situation stabilizes.
Now this is where the situation could have got messy. A pro-Russian"wannabe" breakaway state (at least on paper), with a majority ethnically Russian populace, being threatened with violence right on Russia's own doorstep. The situation is starting to mirror the lead up to the 2008 Russian-Georgian war. However Russia has learned from that conflict and has altered their preventative doctrine accordingly. Instead of waiting for Ukraine to attack Crimea and then inevitably counterattacking, Russia laid out its cards on the table by deploying their forces within and outside of Ukrain. Through doing so they hope to cower the Ukrainian government into inaction and avoiding war in the process.
Neither side wants a war. The only way it could happen is through rash and foolish action undertaken by volatile elements in an attempt to get an easy win where there is none. In 2008 South Ossetia looked like an "easy win" for Georgia and many paid dearly for that illusion. If prior to troop mobilization Sevastopol and other Crimean bases looked "easy" then now they most certainly do not. Using Russian troops for protection of key points of infrastructure such as the Simferopol airport only strengthens their ability to protect the interests of Russia and the Crimean people.
Russia is being very cautious in how it chooses to proceed. So far Russia is following the existing treaties to the letter. No breach of any kind has so far taken place, despite all the media sensationalism. Note that pre-Duma approval, the troops defending the Simferopol airport intentionally don't have magazines in their rifles and no armour has been deployed, their presence around the airport in the current manner does not legally constitute an act of aggression or occupation. They are legally there as an informal peace keeping force. Russian troops are present around the airport, but officially they are not the ones controlling it, the Crimeans are running the show, at least on paper. The Russian troops are currently there in a role of an enabling shield, not a sword. Russian bases have been reinforced within the levels permitted by the 1994 treaty and their troop movements both within and outside of Ukraine are legally in the clear. Russia is taking every step to ensure that they are toeing the line of international laws and treaties.
Although Putin has obtained Duma's approval to deploy troops in Ukraine, so far it is held as a chip to strengthen the Russian position. A chip that has not been cashed in. Doing so without Ukrainian provocation would undermine the Russian position. Russia already has over 20,000 troops legally present within Ukraine. Double the force that was used to defeat Georgia.
In essence this tells us several things about Russian intention:
1) Such caution is not indicative of a country that set out to illegally annex Ukraine. Even without warnings from Western Powers such action would have made no sense for Russia.
2) Russia aims to remove Ukraine's ability to silence the Crimean opposition by force, by legally deploying troops around key Crimean access points and reinforcing their bases Russia is placing their own forces as a buffer between the pro-Russian Crimean opposition and potential use of Ukrainian forces to regain control of Crimea. A Russian show of strength on Ukrainian border is meant to signal to Ukraine that trying to force Russia out of Crimea will have serious consequences. The potential for Russia to instantly pour pre-approved troops into Ukraine further leverages Kiev away from seeking a military resolution.
3) Without the option to use force Ukraine will have to rely solely diplomatic means in order to negotiate with the Crimean opposition. This is greatly advantageous to Russia, the heavy pro-Russian sentiment of the population forms a Win-Win-Win scenario with the following outcomes:
WIN 1: Russia get to use its political leverage over Crimea to ensure that the Black Sea Fleet stays in Crimea in return for facilitating the reintegration of Crimea into Ukraine.
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WIN 2: In doing so Crimean and other pro-Russian views will have to be represented within the new government, thus Russia regains a portion of its political influence in Ukraine.
or
Win 3: Crimea agrees to split away from Ukraine following the March referendum, joining Russia as a fully or semi-autonomous region.
Russia has its foot in the door, thus Ukraine is forced to respect the rights of the Crimean people. The only way Russia loses out is if Ukraine attacks, in that event everyone loses. Russia has been trying to prevent that from happening by flexing muscles to show that any such attack would be suicide.
tl,dr: Russia wants to keep the naval bases in Ukraine as the bottom line, protect the ethnic Russian population and to force the Ukrainian government to seek diplomatic solution in regard to Crimea. Through doing so they either regain some of their political influence within the new Ukrainian government or gain control of Crimea outright. All without firing a single shot.