Art is a message. It has a sender and a receiver. The sender aka the creator has an idea and their synapses create the piece of art. The receiver - even when privy to the thoughts of the creator because they talked or wrote about it etc. - consumes it and has a response. It could be along the lines the creator had intended but it doesn't have to be. Both sides could be equally happy with their side of it while thinking completely different things.

So an artist can try to attach a certain meaning to their artwork but it is no guarantee the audience will see it that way. Is the person in Munch's The Scream screaming themselves or holding their ears to block out screaming they hear? I read what the artist intended and I can tell you I thought the other thing.

So far I've been talking about a single artist and a single consumer. That's not how this works. There could be a group who have differing ideas about the art they're creating, like a song. So it means different things to different people on the sender side already.

It gets really messy on the receiver side because ideally the art will be consumed by hundreds and thousands of people. In that group you will have opinion leaders tastemakers and they in turn will influence other recipients. History also filters artworks. I don't think Leo thought his postage stamp size portrait of a smirking Italian merchant's wife would be the most famous painting in the world if experts hadn't endorsed it, it hadn't forcefully changed owners, hung in Napoleon's apartment, was stolen and recovered. So there are biases built in and it isn't as clean cut as saying everybody interprets it their own way in most circumstances.