While possible, it is unlikely that you would fall to death while climbing Kilimanjaro. Most of the routes on the mountain are non-technical and well-trodden. This means you don’t have to be a professional mountaineer or athlete to navigate your way up them.
However, in the same way that you could potentially take a bad step when walking up a steep set of stairs, the same is true on Kilimanjaro. There are a few areas on the mountain where it is possible to have a bad fall, but as long as you follow the instructions of your guide, the risk is very limited and far lower than on other mountains.
As with all mountains, bad weather increases the risks of falling. It is best to avoid the rainy seasons as slippery paths can make the mountain very dangerous, both for you as well as your porters. The weather can also be fairly unpredictable. For example in June 2018, it is said that unexpectedly heavy snowfall near the summit led to several lethal falls when guides led their clients to continue the climb despite the obvious risks.
With responsible companies and guides, however, such risks are mostly avoidable and most paths on Kilimanjaro are very low-risk – except for the general risk of altitude sickness and the risk of rockfall on the Western Breach.