Demand Response is a mechanism to help balance an electricity grid. Typically, it involves incentives (economic or otherwise) for consumers to move their demand to when supply is plentiful. For example, to move electricity demand from peak times to off-peak times.
Gravity batteries are a renewable energy storage mechanism, still being developed for the mainstream. In theory, they are very similar to pumped hydroelectric. In times of low-demand and cheaper electricity, water is pumped up a hill into a reservoir. When electricity demand is high, and price is high, they let the water fall through a generator using the force of gravity.
Gravity batteries are another take on this principle; store energy when it is cheap and plentiful and generate electricity when it is not - through using gravity.