BTC is a speculative commodity so bubbles are to be expected, and bubbles are cyclical in nature. The previous bubble went up to about US$250 and took several months to build back up and then inflect to climb exponentially to ~1200. There's not one reason for this, and it happens with other bubbles too. But I'll try my best:
The general explanation is that smart money buys low, generates media attention that induces FOMO (fear of missing out) which attracts buyers, who raise the price to new highs, increasing media coverage ad absurdum, when finally there are not enough suckers to keep the rate up and people panic and start selling. Then there's usually a "dead cat bounce" (you'll see the price jumped back up after the first plunge from the peak) followed by more selling. The smart money sells all the way to the top, and buys all the way to the bottom. Now they have to start the cycle again, so they use their market making power to quiet things down and make it feel safe again, waiting for a new crop of people to come back, buy, see amazing returns, tell their friends and media, and the bubble starts again. We're likely there now.
The China factor One main factor leading up to the ~1200 bubble in particular which made it so much higher was the rapid expansion of BTC speculation in China at the time. That's simply a huge market, and New Chinese exchanges were opening up on an almost weekly basis, with relatively low barriers to investment. You could see them leading the price action at the time, and growing their capitalization at a crazy rate. Exchanges like BTCChina and Huobi etc. overtook MtGox's volume in a matter of weeks if not days.
Post-burst Volatility I'm sure there are plenty of reasons for this, one of which is just the general nature of bubbles as explained above. However there were at least a couple of specific things I can think of that contributed to volatility post the ~1200 bubble: Wall Street, media coverage, and the sorry state of exchanges at the time.
Wall Street around that time started giving quants some money to play in the BTC market. You could literally see the bot action taking over MtGox on the way to the top and then back down again. I'm not saying the bots did it, but they do make more money when price movements are wide, and had enough influence on the price to induce these large moves. For example they would create lots of bids at a certain low price with one hand, and begin selling to apply downward price pressure with the other. People would put their bids just in front of the bid wall, thinking it represents a solid price support (a "bottom" for the move). As selling accelerated, the bid wall started receding lower, so they could keep selling into those suckers' bids. Then the wall was removed completely, creating even more panic selling, until the smart money decided it's time to pump the price back up. This, and the opposite ("pump and dump") were happening on a regular basis and observed live by traders on forums like TradingView.
Media coverage was a giant piece of uninformed hype. The price action drew attention, but the stories were more absurd than the price. When some company said they'd accept BTC the price jumped. Then someone talked about taxing Bitcoin and the price tanked. Most stories were non-news or rumors or actual fake stories planted by smart money, but panicky noob traders would buy and sell on it as if it were news about GE or Microsoft, reported in the WSJ.
Finally, Exchanges were constantly beind DDoSed and manipulated, which made small-time traders panic and sell, and then panic and buy back in when the price jolted back up. Once the largest exchange by volume, MtGox exploded in slow motion, causing many ripples along the way (mostly in the weeks following the ~1200 peak). Exchanges would frequently go illiquid and disappear with your money. Exchanges were so badly run they would constantly make you feel like your orders aren't being processed and induce panic. This adds volatility.
I'm sure there's plenty I'm missing, happy to see more comments/answers!