Every object has mass and anything with mass has gravity. We only notice the effect with big things, such as planets and stars. An apple has a gravitational field but it is so tiny that we are unaware of it. Drop the apple and it falls to Earth. This is because the gravitational field of the planet is millions of times more than that of the apple so the effect provided by the apple is drowned out. It exists though.
Now, think about the Earth and the moon. Common understanding is that the moon orbits the Earth. This is not strictly true as they actually orbit each other. The point around which they orbit is about a mile below the surface of the moon.
We all know that the moon exerts an influence on the Earth. This is most obvious with ocean tides where the sea is pulled around depending upon the position of the moon. This is an example of one objects mass, the Earth, being affected by the gravity of another, the moon. Meteors pulled in by Earth’s gravity and increasing its mass, provide an example of how an object’s mass is affected by its own gravitational field.