Means butting into something that’s got nowt to do with you, usually with unwanted advice or commentary. The picture is someone literally shoving an oar into a boat they’re not rowing, then acting like they’re steering. Mostly said as a telling-off, because nobody’s asking for a random referee turning up to stir it.
"I was just having a moan about my flatmate, then Dan pipes up with a full TED Talk. Mate, don’t stick your oar in, pass the biscuits."