Recall that gravity is an inverse square law force, so at very small distances, the strength of gravity around a point mass becomes very large. But objects far enough away will not sense anything unusual. For very strong gravitational fields, Newton's description of gravity becomes inadequate. Einstein's theory of General Relativity must be used to describe the gravitational effects. Einstein found that gravity is not a force in the usual Newtonian description of force.
Gravity is a result of a warping or distortion of spacetime around a massive object.
The stronger the gravity is, the more the spacetime is warped or curved. I discuss the developments of the concept of spacetime and the theory of General Relativity in the Einstein's Relativty chapter . That chapter also gives several observations of curved spacetime. The definite discovery of a black hole would provide more evidence for General Relativity. Within the event horizon space is so curved that any light emitted is bent back to the point mass.