Caught it

For several days, I've been noticing something on the gate at the entrance to my house.It looked like butterfly cocoons.I saw caterpillars moving around there, and I had never seen this process up close before.I didn't clean the gate — it's quite dirty — because I didn't want to disturb them.Today, I was happy to find a butterfly (I think) that had just come out of its cocoon.

What do the butterflies tell me?
That everything is okay, that I am safe.

And what do I tell the butterflies?