Symbian collapsed because Nokia abused their power over S60 and the Symbian Foundation to maintain their market leading position. When Android appeared on the scene it offered an alternative platform for manufacturers to use. It quickly became clear that it was just as capable as Symbian. If manufacturers chose to, they could develop their own platform on top of it (much like UIQ on Symbian) or they could go with Google's platform, offering a ready-to-go solution that could be customised (much like S60 on Symbian). Because of this, other manufacturers abandoned Symbian for Android. It took a few years, but it happened.
Meanwhile, Nokia were doing their best to commit suicide. Long story short, they didn't react quickly enough to the iPhone and the consequent shift to touch screens. At the start they just mocked the idea, and the iPhone. Then they shoehorned a touch UI on to the new version of S60, releasing it on poor, unreliable hardware (5800 Xpress Music, N97). These early Nokia touch screen handsets sold well, consequently turning a lot of long-time users off the brand. They limped on with this poor UI for almost 3 years, refining it but not really succeeding in creating a good user experience (you can't polish a turd). By the time they announced Symbian S^3 (a new, touch screen focussed successor to S60) many had lost interest. By the time they got the N8 out (late 2010) they had lost the market. The N8 and S^3 were nice enough, but they seemed like they were designed for the market as it was in 2008, not the market of 2010. By this point, Apple had the iPhone 4 with retina display, and iOS had multitasking. Android had most of it's kinks worked out and had received a few hit phones of it's own (HTC Hero and Motorola Droid in 2009, HTC Desire and Samsung Galaxy S in 2010). The N8 and Symbian S^3 just didn't match up. By now the most common question was 'where are the apps?'.
Nokia pretty much gave up on Symbian's high-end aspirations at that point, shifting the focus down the market. As it stands today, S^3(/Anna/Belle) is pretty much dead, thanks in no small part to the plunging hardware costs that have allowed Android handsets to chase Nokia in to the lower realms of the market. The past 18 months have seen Symbian sales fall apart.
TL;DR? Symbian is no longer a big player because Nokia didn't adapt S60 fast enough to the rapidly changing market conditions, while Android offered other OEMs a better platform than they had with Symbian under Nokia's tyranny.
