This is a big question and it is also important for climate studies and I am only going to answer it in simple terms but let’s not forget there are quantitative answers at global scales.
When the wind blows onshore it moves the surface water towards the shore. If the shore is a wall like a harbour wall then the moving surface water raises the water level at the wall. This raised water level at the wall puts pressure on the deeper water below (which moves away from the base of the wall to regions of lower pressure or away from the wall at the bottom). The water at the wall moves downward to compensate and this is called downwelling. More surface wind (stress) and more downwelling.
When the wind blows off shore. The surface water moves away from the wall. Sea level falls at the wall and water rises up the wall from the bottom. This is called upwelling.
Ekman worked out that in the open ocean the transport of surface water moves to the right of the wind direction due to the effects of the Earth’s rotation (in the northern hemisphere). So when the wind is parallel to a shore there will be upwelling or downwelling depending on the wind direction. Imagine a straight shoreline aligned towards the south (or north). If the wind blows to the south (from the north or a north wind) then the surface water moves offshore to the right of the wind and upwelling occurs.
These upwelling regions bring up cooler water rich in inorganic nutrients and surface phytoplankton growth is increased. This happens particularly seasonally off West Africa and Venezuela. There is also Equatorial Upwelling with zonal wind so some corals won’t die out so quickly with global warming.