An explanation I like, from michaelochurch:
Let's say that you have 20 tasks. Each involves rolling a 10-sided die.
If it's a 1 through 8, wait that number of minutes. If it's a 9, wait 15
minutes. If it's a 10, wait an hour.
How long is this string of tasks going to take? Summing the median time
expectancy, we get a sum 110 minutes, because the median time for a task is
5.5 minutes. The actual expected time to completion is 222 minutes, with 5+
hours not being unreasonable if one rolls a lot of 9's and 10's.
This is an obvious example where summing the median expected time for the
tasks is ridiculous, but it's exactly what people do when they compute time
estimates, even though the reality on the field is that the time-cost
distribution has a lot more weight on the right. (That is, it's more common
for a "6-month" project to take 8 months than 4. In statistics-wonk terms,
the distribution is "log-normal".)