Understanding gravity helps use know how objects fall to the ground and how objects are attracted to one another.
Here is a great video on gravity and how it affects everything from free fall to orbiting planets.
There are two important formulas that the video talks about. Here are links to pages that have more information on the acceleration of gravity and the gravitational force between two objects. But why are these important? Let's look at the applications of Newton's second law and the equation for gravitational force.
Orbiting Planets and moons
It is important that we understand gravity because it gives us an understanding for why the moon is orbiting Earth and not flying off into deep space. It also helps us understand other forces the moon has on earth like the tides.
This is most likely one of the most practical applications of the laws of gravity as it helps us understand everything from...
and most significantly
Yes, Newton's second law is the basis for getting us the the surface of the moon. So how are we going to apply this? Let's start dropping stuff and experimentally find how strong gravity is.