The verbalisation of a noun where an an activity is done.
In this case, "market" is the place/noun and that the activity of grocery shopping is done at the market. Market is then verbalised by adding "-ing" = "Marketing"
Simply means : Grocery shopping, traditionally done at the market, nowadays supermarket is also acceptable as long as it is to do with shopping for grocery, not just picking up a carton of milk.
Commonly used in Singapore and Malaysia.
Nothing to do with the meaning of a profession to advertise a product or service.
Friend1 : Where is your mum?
Friend2 : Marketing
Friend1 : Huh?
Friend2 : She's gone to the market to do buy some grocery for the week.