Why did he push for elections? Why would he voluntarily dissolve communism? Was there a any clear plan about how Russia would transition to a new government?
Also, on an unrelated note was it true that the early USSR was more egalitarian than the U.S.?
I'm not a professional historian, but I think I can have a decent crack at this.
First of all, it's extremely important to know that Gorbachev absolutely did not voluntarily disband the the Soviet system. He remained committed to the idea of Marxism-Leninism and to the idea of a union of socialist states throughout, although in modern times he has become a Social Democrat of sorts. With that in mind (and I will come back to this point later on) lets dig in.
It's important to realise that Gorbachev was quite different, both as a leader and a person, from previous leaders of the USSR. He was relatively young (54 I think) when he become General Secretary, and was the first and obviously only leader of the USSR who did not live through the Revolutions as well as the only one who was not an adult during of WW2. Historians (I can't think of names at the moment) have argued that, on a personal level, Gorbachev did not feel it necessary to be confrontational with the West a means of self-protection, which harkens back to the establishment of the Eastern Bloc after WW2 as, largely, a buffer zone against invasion from the west.
Whether this is true or not, obviously I can't say but Gorbachev was exceedingly open with the West from the get-go. Margaret Thatcher, a Cold War Warrior if there ever was one, famously called him a "man one can do business with". This attitude led to quite a remarkable working relationship between him and President Reagan, with a number of mostly productive summits between the two from 1985 onwards.
Gorbachev was also quite keen on modernising the USSR. The two main "policies" (really multiple policies and actions under two banners) were Perestroika and Glasnost. Perestroika was a political and economic restructuring of the Union, along the lines of increased democracy in the political process and degree of market liberalisation. Glasnost was a term, meaning "openness" in Russian, used to describe the drive to liberalise Soviet society, with restrictions on freedoms, which had been quite significant during the Brezhnev era, being lifted or reduced.
So for all this talk about how Gorbachev was a reformer, he certainly was not aiming to entirely Westernise (for want of a better term) the USSR, nor was he willing to abandon socialism/Marxism-Leninism. I believe the predominant view of historians (again, I'm so sorry I can't give any sources or names, it was quite a long time ago since I studied this) is that Gorbachev's liberalisation reforms essentially opened a Pandora's Box within the populace, with the desire for more freedoms/change becoming too great to be ignored.
Equally important is the wider context of Soviet society at the time. I don't know much about the economy, but essentially it was screwed. In addition to this, the Soviet experience of the Afghanistan War SEVERELY lowered moral within the USSR, to the point where it's often been referred to as the Soviet's Vietnam. The Soviet peoples were not happy, so when Gorbachev comes along offering what essentially was duct tape on a massive water leak, the people wanted so much more. Gorbachev's rampage against alcoholism also didn't help make him any more popular. Interestingly, Gorbachev is still very unpopular in Russia today.
This dissatisfaction with the system led to a series of revolutions (mostly peaceful) in Eastern Bloc countries, where essentially the Soviet-backed governments were removed from power (or, in the case of Hungary, voluntarily reformed themselves) and replaced with liberal populist governments, headed by the key figure of the individual movements in those countries. During this period, the USSR lost Poland, Czechoslovakia, East Germany, Hungary, Romania and many others.
The final nail in the coffin for Gorbachev and the USSR as a whole was when he was saved from a coup by Boris Yeltsin in 1991, who was a popular leader and critic of the Soviet regime, who went on to become the first president of Russia. The coup was launched by conservative factions in the Politburo (the Soviet high command), who wished to undo the reforms introduced by Gorbachev while he was on holiday. Having been saved from this by Yeltsin (which involved him climbing into a tank, I believe), Gorbachev's power was severely reduced and it became clear that it was the Yeltsin populist faction which really held power. After the coup, a wave of regions of the USSR declared independence, most notably Ukraine. At this point there was literally nothing Gorbachev or the Soviet government could do to restore order, add the people had just stopped playing ball. The game was already over, the Yeltsin faction had made Russia all but independent of the USSR (and actually declared independence on the 11th December 1991, leading Gorbachev to "voluntarily" dissolve the USSR on 26th December 1991.