In Newton’s original model, gravity acted instantaneously. A few physicists like Laplace tried to model gravity as a fluid, with a finite speed, but they didn’t know what the speed should be. Einstein realised that instantaneous gravity would violate the fixed speed of light, because this would transmit information faster than the speed of light: this was one of the starting points for General Relativity.
In General Relativity, gravity acts at the speed of light. This is because the speed of light gives a particular intrinsic relationship between time and space.
In a future Quantum gravitational theory, the speed of gravity will be the speed of a graviton. But most theories expect the graviton to be massless, and massless particles always travel at the speed of light. So we expect the speed of gravity is indeed the speed of light.
David has given the answer to your question. One thing I like to imagine is this. If, hypothetically, the Sun instantaneously stopped existing (which, is just the hypothetical set-up to allow us to think about some actual physics), then the Earth wouldn’t do anything differently for 8 minutes. That is, it would carry on going round in its orbit for 8 minutes. Note that 8 minutes is the time it takes for light from the Sun to reach the Earth.