A diffraction pattern is the physical term for what you see when looking at a star through a telescope at high power under good seeing conditions (steady atmosphere with little air turbulence). Simply put, it is the concentric bull’s-eye pattern of the stellar image you see in your high-magnification eyepiece.
Because even the closest stars are so very far away, they will never show a real disk or ball shape in a telescope. However, on steady nights at magnifications around 60x the aperture of your scope in inches (for example, 240x for a 4 in scope), you’ll see the star as a tiny disk surrounded by a concentric ring or rings (assuming quality optics that are properly collimated or optically aligned). This bull's-eye is called the diffraction pattern of the star; it's created by the interaction of light waves from the star with the circular edge (aperture) of your lens or mirror. The central bright region is the Airy disk and the surrounding bright circle is the diffraction ring.
The Airy disk becomes smaller as the aperture of the telescope gets larger. In theory, when you double aperture, you also double resolving power, since the Airy disk is only half as large. Two points of light--a double star--can be distinguished more closely with the larger scope. Since the disk is only half the diameter, it has 1/4 the area of the disk seen through the smaller telescope. In addition, when you doubled the size of the mirror or lens, you increased the area and light-gathering power of the scope by four times. So four times the light is in an area 1/4 as big, so the star appears 16 times as bright. This is why fine details in large telescopes jump out compared to the same view with a smaller telescope.
The illustration below shows Airy disks for a faint double star as viewed with a 4 in and an 8 in telescope. (Darkness in the drawing means a brighter disk.) Look at the two drawings for 1000x. Note that the 8 in disks compared to the 4 in disks are smaller and much brighter, so the double star is cleanly separated, even showing a third star that would not have been visible with the smaller scope.