What does it mean?
A play on words: if you split "impossible" into "I'm possible", the word seems to say the opposite of what it means. The message is to stay positive about what you can do.
Who said it?
Audrey Hepburn: British actress and humanitarian (1929–1993).
These exact words are widely credited to Audrey Hepburn, but they don’t appear in their known work. They may be a later paraphrase or a misattribution.