Means the food is so tasty you keep going back for another bite, even after you promised yourself that was the last one. Usually used for crisps, biscuits, sweets, or any snack that has you hovering by the cupboard like a feral seagull. Handy little word when you want to confess greed without sounding too tragic.
"These chocolate hobnobs are proper moreish, mate. Said I'd have one with my tea, now the whole packet's been demolished and I'm stood there like a right mug."