What is gravitational potential energy? Why is it negative?

We define gravitational potential as: the work done to bring a small "test" mass from infinity to a point. But what does this truly mean?

1. The "work done" is simply the energy we need to put in if we wanted to do an action - for example, lift something from the ground to a shelf, or move this mass in a gravitational field. As for "test": All masses must have a shape and other properties like charge. But we dont want to have to think about how charges get changed if we start moving the mass or how its shape affects gravity. We can pretend (reasonably) that the mass is a test mass: one where the shape/charge and other properties dont matter, and ONLY the mass and its separation r is important.

2. At a separation (say to Earth) of infinity (r=infinity), the energy of a mass is 0. 0 is an important number, so this separation is an important separation and why we use it in the definition. At a separation of the surface of Earth (r=6400km) gravity wants pull the test mass closer and closer. Its gravitational potential energy wants to pull it closer and closer. To do the opposite (ei, move a test mass from a point TO infinity) we need positive amounts of energy (like when we lift something up onto a shelf, or shoot a rocket out into space really far). But as we said what the gravitational potential energy wants to do is the opposite! So the work done by gravity is NEGATIVE. The gravitational potential energy is negative because us trying to do the opposite of what gravity wants needs positive energy.

There is also the deeper reason why it is negative, due to integration, but that's what you need to know.