A gravitational field is the tendency at each point in space to force things in a particular direction. Mathematically, it is a vector field, a function on the three dimensions of space yielding a vector in the direction of the force with a magnitude consisting of the amount of force applied to an object at that point per unit mass of the object. Or equivalently, by Newton's law F=MA, the vector matches the direction and degree of acceleration of an object at that point. This field is the gradient of the gravitational potential, the force being toward the lowest potential, which is typically represented by negative numbers, the nearer the object(s), the more negative. A region of space that has such low gravitational potential, such as the space surrounding and object, is termed a gravitational well.
In a universe with a single point-size massive object, the field would be spherically symmetric around it, the magnitudes adhering to an inverse square law, and the direction of the object. With two or more, there are places between where the forces balance each other, but from a great distance from them all, the magnitude of the field vector would approximate that of a single point with the sum of their masses.
General relativity (GR) complicates this picture: the above can be referred to as a classical gravitational field or Newtonian gravitational field. The measurement precision to distinguish the differences imposed by GR is high except in circumstances extreme compared to what we experience on Earth.