Can someone explain why this is better than just using pumps to pump water up from the reservoir and extract the energy with when the water returned back?
Pumped water only works if you have the right conditions. I.e. you need a certain altitude difference and enough space to have an upper and a lower water storage facility.
Pumped water storage is very efficient and an established technology, so when it's possible it's a good choice, but it's not possible everywhere.
It's not, but it doesn't require a giant reservoir next to a 100m+ elevation change. Almost all of the really good locations for dams already have them, and their water discharge rates are driven by a lot more than just power generation.
It requires less surface area, both due to compressibility and due to hydrodynamics. Additionally, water is a strong erosion source, air is not, so this can make use of existing excavations much easier and deep excavation is very very expensive.
not a lot of places have enough terrain to create a lake, plus in some places there's already shortage of water so removing it from usage would be pretty bad
Pumped water storage is very efficient and an established technology, so when it's possible it's a good choice, but it's not possible everywhere.