Orbital mechanics is the application of physics to understand and predict the motion of objects in space, particularly those following orbits around celestial bodies, whether that be the Moon, Earth, or any other object with gravity.
Instead of travelling in straight lines, objects in space will always follow curved paths called orbits, which are determined by the forces acting on them. With the right direction and speed, an object can keep circuling around an object without hitting its surface. Think of orbits as a continuous freefall, where the object is being pulled down but has enough speed to avoid crashing.
Gravity is the fundamental force that governs the motion of objects in space. It is the attraction force between two masses, keeping planets in orbit around a star and moons in orbit around a planet. It can also be imagined as an invisible tether.
All celestial bodies with sufficient mass generate a gravitational field. The heavier the body, the stronger the gravity will be, requiring more speed to stay in orbit.
An orbit is a curved path that an object will follow around a body if there is a balance between velocity and gravity. Orbits are almost never perfectly circular, although you can get close. The most common orbits you will see are elliptical orbits and circular orbits.
The idea of elliptical orbits was actually first proposed by Johannes Kepler, who showed that planets don't move in perfect circles.