The world outside of your quaint colony is big. A lot is happening and some of that can spill over into your little world. These things manifest as events that you can usually respond to in at least two ways. What you decide to do will have an impact on your Citizens. Some decisions more than others too as some of these events can stir up quite a fuss and cause social tensions in your population.
There are also events that occur locally, in your town, like a massive fire, or a great crop season etc. Anything can happen.
Event triggers are time-based, meaning that after an event occurs, it will take some time before the next one can happen. There is random chance involved since an event (any event) can, but doesn't have to happen. The possibility of an event happening additionally relies on a number of factors, especially on the condition of various city stats (stockpile levels, number of citizens, citizen class distribution, social issues state...).