what does i can do it better mean?

it mean i can do it better than YOU!

it totally depends on the situation.

Doing it better implies there is a reference to how it has been done already. It could be better than when you did it, or someone else.

If the last time was lousy, then you can still be rubbish but be better, so it would not automatically mean it is done well. However, the inference from the statement would suggest is is at least to some acceptable standard.

That depends on the situation. If used as lyrics in a song, I’d say you’re correct. If said after you made a huge mess, it probably just means that your normal level of quality is usually much higher.

No, it’s comparing how you do it with how someone else does it, or how you did it before.

Either:

Jim did a good job acting as Romeo, but I can do it better.

I did pretty well on my rough draft, but on the final paper I can do it better.

It means that you can be better than you were last time you did it. Better=Smarter, Quicker, etc

It must mean, I can do it better than anybody else.

In this instance I don’t think better means well.

It means there is room for improvement.