If you have reservoir hydro (rather than run of river), what we mean here is that you can effectively "store" the excess wind production by just not running the hydro units, holding the water until later when the wind dies down, and then running the hydro then. That's what's happening now in the Nordic system, as well as the Pacific Northwest of the United States and New Zealand and other hydro-rich regions. It's technically not storage I suppose, at the full grid level. I just mean that Denmark can export power to Norway or Sweden, which back off of hydro production, and then later it can import power from said hydro dams when the wind dies down.
This is similar to how people with solar on their rooftops often use the grid as a "battery," exporting solar during the midday peak and importing from the grid in the evening. It's not really storage, just taking advantage of a much larger, flexible system.
Both examples aren't truly storage. That's why we put it in scare quotes ("store"). Sorry if that wasn't clear.
Pumped hydro amounts to true storage: you use excess electrical generation to pump water up into the reservoir and then release it later when needed to generate electricity.