The Sun rises and you notice that the seat of your garden bench warms up. At the same time, you notice that the driveway asphalt warms up. That is a simple example of correlation.
It would be a mistake to think that if you warmed up the garden bench, your driveway asphalt would warm up… causation. The cause of the warmed up asphalt is, of course, the Sun… not the warm garden bench.
For a more interesting example: Yesterday, Bill and I placed a Shiva Linga in the waterfall. I told Bill that should bring some good luck. Then with a smile, I told him I was going to make a phone call to see if it worked. For months, I was hoping for a particular thing to happen and I would call and see if there was any good news about it. And then, eureka, it in fact happened! The phone call brought the good news.
Now here we need to be careful. Firstly, the good event actually happened BEFORE we placed the Linga, so causality between the two is not a possibility. Secondly, of course, we do not know for sure that it was not just a coincidence; so we certainly do not KNOW that a correlation phenomena occurred. That is to say, both the Linga placement and the good event could have occurred as the result of some other causal event they had in common (similar to the Sun rising causing multiple things to warm up); or it could have just been a coincidence.
However, this sort of thing happens a lot. We do a havan and come home to good news regarding the intent of the havan. Or as happened recently, someone receives a gemstone recommended by his jyotishi and immediately the desired result occurs. At some point, you have to begin to understand the principle of correlation on a more cosmic level than the garden bench and driveway example.
Then the inevitable question arises: Would the good news have come if the Linga was not placed? Would the desired result have occurred if the gemstone was not received? Well, just ask yourself this: Would the driveway have warmed up if the garden bench did not?