Step 1: a train gets delayed for a minute somewhere on the line. A dozen common reasons exist- someone becomes ill, mechanical issue, debris on the tracks, etc.
Step 2: Because it's rush hour, there's minimal buffer time between trains so the train behind it must also stop (and the one behind it, and the one behind it, etc). Even a 60 second delay of one train can back up the whole line.
Step 3: Because a train is late, there's more people trying to get on and off, which makes it take more time per station. As well, with more people per train, there's more human-related delays per train. The additional delays mean "go to 1".
With large enough buffers between trains, the system is stable- the problems get smoothed out. With small buffers, like during rush hour, the system can get into a feedback-loop total system failure. A 30 minute trip becomes hours long.