What does it mean to see a grasshopper on doorstep?

It means a grasshopper is on your doorstep. That's it.

He was probably happily hippity-hopping along in the grass, as grasshoppers do, then all the sudden the grass ran out and he was confronted with a door and he thought "damn humans, building stuff on my grass!"

Seriously though, superstition has been disproved by hundreds of scientists all over the globe. The fear or belief that something will happen is caused by ourselves, not other things in the world.

For example if you break a mirror and think "oh no I'll have bad luck now!" and really believe that you will have bad luck - then you will have bad luck because you are expecting bad luck, so you unconsciously make it happen yourself.

If you break a mirror and say "oh well, I'll buy another one" and not believe it will cause bad luck - it won't. You'll just have a nice new mirror as a result.