The angular resolution of a telescope is set by the diffraction limit, and it defines the smallest angular scale that a given telescope can observe. Put another way, the resolution limit of a telescope sets the minimum separation of two objects that can be distinguished.
To understand why diffraction occurs, we must first understand Huygen’s Principle (1678), which states that given the wave nature of light, any point on a wave front can be considered the source of secondary wavelets or spherical waves. The surface tangent to all of the secondary wavelets defines the location of the wave front at some later time.
Young and Freedman, University Physics with Modern Physics
Diffraction occurs when light bends as it passes through a small opening or aperture. Consider for example a plane wave front incident on a narrow slit or opening. At each point in time before the wave encounters the slit, we can decompose the wave front into a series of wavelets, but the surface tangent to the wavelets remains unchanged and we still have a wave front propagating as a plane.
As the wave front encounters the slit, however, wavelets on either side of the slit are blocked. Only wavelets near the slit pass through, which means we no longer have the wavelets on the edges of the plane wave contributing to our wave front, and so the surface tangent to the wavelets that make it through the slit is no longer a plane. In other words, the light bends and spreads as it passes through the slit.