Each resident of your city has a fixed life span. It begins the moment he moves into town and ends with the demolition of his house or his death.
The crucial point here is that every citizen who lives through the full life span lives exactly the same length. So if nothing comes in between, neighbours in the city move in at the same time and also die at the same time.
This creates a special phenomenon: The death waves. In newly constructed residential areas with high demand for residential zoning, all residents will move in at the same time. Accordingly, they will all die almost simultaneously at the end of their lifespan.
Death Waves: The Consequences
You can recognize a death wave by the amount of skulls displayed above the houses. In the statistics, the death rate then skyrockets. A death wave can turn an entire district into a ghost town in a very short time. Then you have to demolish the abandoned houses and provide enough ambulances and free cemetery spaces, if not already done.
The sudden drop in population will significantly reduce your tax revenue. It is therefore important to always have a good amount of savings beforehand in order to overcome this period.
How to Fix Death Waves
Death waves evolve when a huge amount of residents, that moved into the city at the same time, die, because they reached the end of their live span. In order to prevent such a death wave, residential areas have to be zoned slowly, so that the population later also dies evenly.
Often, however, new residential areas are planned in one step and then all streets are zoned with residential areas at the same time. This results in large death waves later in the process.
There are also mods that help against death waves. The mod Lifecycle Rebalance gives new residents of your city a random age instead of always the same age. It also adds some random factors that can cause the sudden death of your residents. This way, the death rate is much more constant and therefore has fewer upward swings.