the gravitational field
Instead of asking how two specific masses pull on each other, physicists often prefer to ask: what does a big mass do to the space around it? The answer is that it fills that space with a gravitational field, an invisible readiness to pull on anything that shows up. Picture the Earth surrounded by arrows, all pointing inward, telling any object placed there which way it will be tugged and how hard.
The field strength, written g, is defined as the force per unit mass: g = F / m. Its direction is toward the source mass, and its magnitude at distance r from a mass M is g = G M / r^2. The units are newtons per kilogram (N/kg), which is exactly the same as metres per second squared (m/s^2). That is not a coincidence: because g = F / m and Newton's second law says a = F / m, the field strength at a point equals the acceleration any freely falling object gets there. At Earth's surface g is about 9.8 N/kg, or 9.8 m/s^2.
The field idea explains something Galileo noticed: in a vacuum, a feather and a hammer fall with the same acceleration. Since every object at a given point sits in the same g, and each gets acceleration a = g regardless of its own mass, they all speed up together. The field is a genuine feature of the space itself; it is there whether or not you place a test object in it to feel the pull.
On the Moon g is about 1.6 N/kg, roughly one-sixth of Earth's. A 60 kg astronaut therefore weighs F = m g = 60 x 1.6 = 96 N there, versus about 588 N on Earth, which is why moonwalkers bounce so easily.
The astronaut's mass is unchanged; only the local field strength g, and therefore the weight, differs.
Field strength g (in N/kg) is numerically the same as the free-fall acceleration (in m/s^2) at that point, because both equal F/m.