This means to get rid of something that you don't want any more by giving it to someone else, while being dishonest about it. E.g. "I can't believe they palmed off that broken Nintendo on me!" (They sold me the Nintendo, giving me the impression that it was a bargain and a good thing to buy, but they were just trying to get rid of it because it was broken). For a transcript (soon) check this page on my website http://teacherluke.co.uk/phrasal-verb-a-day/111-to-palm-off/