The simplest way I can think of this is saying that the bull run is the gaining time and the bear run is the losing time. So a bull run means a time where a cryptocurrency (like Bitcoin), or even altcoins are appreciating in their price again. And the bear run would be the exact opposite. So if you want to invest, you’d want to buy when it’s going down and sell in the bull run (which is what people are doing).
Great analogy but a bull market is simply a period wherein most of the crypto market prices are in an uprise movement simply because many people are buying. Interest means demand, if something is being anticipated to generate profit then it could trigger such thing in this industry. FOMO could result to a sudden and a bit continuous price increase. Manipulation could result to a short term increase. While in bullmarket, it could be for months or for a year, the market prices are breaking 'ceilings' or previous market price "high".
The event could be news related, adoption by many companies, progressive development in this industry or anything that could create a 'hype' for this industry. It is something which will sound or actually be good for blockchain technology in parricular with crypto space.
One good example is Bitcoin halving. Its previous occurence resulted to increase in demand and volume to this industry in general. Now that it is again being anticipated, many investors are accumulating. The act of buying creates a tide pushing other people to also do so and so forth.