meaning

I had a conversation about meaning last week.
Where does meaning come from?
If I make something with a very specific meaning in mind, and give it to someone else, they'll find their own meaning in that thing. The meaning they impart to the thing will be different from mine, even if I do my best to explain what my meaning for it is.
Is my meaning more important because I was the creator?

Is the meaning that Picasso put into one of his paintings more important than the meaning I derive from looking at it?