Previously, we’ve seen that the gravitational field of a point mass or a spherical mass looks like this.

Now, here is the Earth and here are its gravitational field lines. 

It’s a radial field because the Earth is approximately spherical.

The field lines are closer together here than here.

And we’ve seen that this means the gravitational field is stronger here than here.

Next, if we zoom in until the ground looks pretty much flat, we can see that the field lines look almost parallel to each other! 

And the lines are the same distance apart here as they are here! 

So when we’re zoomed in this much, the field looks pretty much uniform…

…and this makes sense, because we’ve seen that near the surface of a large mass like a planet, gravitational field strength doesn’t change significantly with height.

On the other hand, over larger distances, the field is radial and g varies with distance!

So, in summary…

The field around a spherical mass like a planet is…

The field around a spherical mass like a planet is radial so the gravitational field strength depends on distance.

But close to the surface of the planet, the gravitational field appears…

Close to the surface of the planet, the gravitational field appears uniform so using a constant value for g is pretty accurate.