Interference (specifically, wave interference) is the result of interaction of waves passing through the same region of a medium, i.e., the same type of waves (e.g., sound versus light) though they may be at different frequencies. Given known wave patterns, the interference can be predicted (generating known interference patterns) and conversely, the resulting pattern can be analyzed, which is the basis for interferometers, used with electromagnetic radiation such as radio and visible light. Constructive interference is that in which peaks coincide producing a larger oscillation, and destructive interference is that in which peaks sit on top of valleys, canceling each other out, and the oscillation is absent. When waves are crossing each other at an angle, these kinds of interference appear alternately, producing a characteristic striped pattern: this, given the redirection of light through diffraction is what forms the concentric stripes of Airy disks.
The term interference also refers to unwanted contamination, such as radio frequency interference. At some level, this is the same mechanism, but can often be thought of as one signal overpowering another.