1. It's free.
2. It conserves water in general
3. Tap water contains a lot of Ca-ions and Mg-ions: good for human bones, but not too good for a plant if used in excess.
However, plants like Nitrogen very much! And that's where the rain water comes in.
Our atmosphere consists of about 21% Oxygen and 78% Nitrogen, but plants can't take it in through the atmosphere. They need nitrates. If lightning strikes through the atmosphere, it gives the oxygen and nitrogen molecules enough energy to form nitrates, which are NO3-ions. These ions react with the water and form a weak solution of nitric acid. The plants then take it up, via the water.