Almost any town and village in Tenerife has a market where you can buy fresh fruit and vegetables. But there are actually two types of markets in El Medano: the farmer's market and the weekend market with souvenirs, crafts and other types of random things to buy.
A small produce market, selling mostly fruits and vegetables grown locally. You can buy local fruits and vegetables, meat, fish, dairy products, Tenerife wines as well as bread and sweets.
This market is smaller compared to others on the island, but it has a chilled hippie vibe, very different from Los Cristianos market for example.
Here you'll find mostly handmade stuff, from jewelry to clothes or other types of souvenirs.
If you're coming from another resort to visit El Medano, you can plan your trip to be on a Saturday so you can visit the market, then have lunch near the beach and simply enjoy the lovely atmosphere in town.
It is easy to come to El Medano from Los Cristianos by using public transport: just take either bus 470 or 483 and you'll be there in no time. So save the taxi money and buy yourself some nice souvenirs from the market or a lovely lunch in one of the bars or restaurants near the square.
If you're coming by car, keep in mind that it gets busy on market days, so finding a place to park might be difficult.
SEE ALSO
Yes, there are in fact 2 markets in El Medano: one which is only for food products like cheese, vegetables and fruits and another which is for souvenirs, clothes and other items.