Imagine you are CEO of a construction engineering company that is traded publicly and whose business is cyclical (or earnings fluctuate widely according to variations in the economy or the cycle of the seasons).
Alright, now imagine the Stock Market sells off on fears of an upcoming recession. What do you do? Well, you may cut investments in that new plant you were planning on building or put a freeze on hiring.
Now imagine, that your competitors, suppliers, and customers hear about this. This type of stuff starts to feed on itself then forecasts are lowered. This becomes self-reinforcing.
This is a simple example of how a sell-off in stocks can cause a recession.