Scattering experiments (x-ray or neutron) generates images which can be thought of as the Fourier transform of the material's realspace structure. I.e. the image is a slice through a conceptual 3D reciprocal-space. Although a scattering pattern can be arbitrarily complex, there are usually various features that can be analyzed separately, and from which one can learn much about a sample's structure. In particular, samples with well-defined structural order give rise to distinct scattering features, such as sharp rings or even distinct spots on the area detector image.
Many samples will exhibit diffuse scattering: scattering intensity over a broad range of angles, without a distinct peak or maximum. This kind of scattering usually comes from disorder within the sample. For instance, low-q diffuse scattering can come from nanoscale or microscale porosity, or from surface roughness in GISAXS. High-q diffuse scattering can arise from the defects in atomic lattices (and from the thermal motion of atoms in a lattice). Although one can generally assign diffuse scattering to some kind of disorder, it is difficult to make an unambiguous link, because there are many effects that can generate diffuse scattering.
A sharp spot on a 2D detector is typically a Bragg peak: i.e. diffraction at a well-defined angle due to a realspace lattice. An array of sharp spots typically indicates that the sample is a single-crystal (or at least oriented; e.g. in-plane powder).
A ring typically indicates an isotropic material generating Bragg peak that is spread orientationally. Thus, the sample is poly-crystalline, with crystallites at every possible orientation, but with a well-defined unit cell giving rise to diffraction spots. These spots are smeared orientationally, giving rise to a set of distinct rings. The ring position can be converted into a realspace repeat distance (e.g. to determine a packing distance). With enough rings, one can determine the unit cell symmetry (i.e. it becomes a powder diffraction experiment, from which one can fit the crystallographic symmetry).
A very broad ring (or halo) indicates a poorly ordered system, with very small grain sizes. For instance, the sample may be poly-crystalline, with very small grain sizes. Alternatively, the material may be essentially amorphous, with the ring indicating a preferred local packing distance, but no long-range coherent order.
A sharp ring that is speckled indicates that the material is poly-crystalline, but the grains are exceptionally large. As such, only a small number of grains within the scattering volume satisfy the Bragg condition, leading to just a small number of spots. A sharp, speckled ring thus indicates a highly ordered system, with large grains. (The ring graininess can be quantified to measure grain size.)