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A gravitational field is the tendency at each point throughout space to push things in a particular direction due to gravity. The entire physical field can be described by a vector field, a function on the three spatial dimensions yielding a vector with 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, a vector matching the direction and degree of acceleration of an object at that point. This vector field is the gradient of the gravitational potential, gravitational force at any point being toward lower potential; the potential is typically represented by negative numbers, more negative nearer the object(s) producing the gravity. A region of space that has such low-valued gravitational potential, such as the space surrounding and object, is termed a gravitational well.
In a universe with only 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 that would reveal the differences imposed by GR is very high except in circumstances extreme compared to what we experience on Earth.