An extended source is an astronomical object which, as observed, has an angular size so as to cover an area of the celestial sphere rather than appearing as a point with no size, the latter termed a point source. Whether an object is one or the other depends on the telescope's angular resolution, so an object might be an extended source for one telescope but a point source for another that has a lower angular resolution.
In radio astronomy, where telescopes have generally been single pixel, the term extended source has generally been taken to mean the source extends beyond the beyond the radio telescope's FOV (i.e., its beam), in which case the strength of the signal is taken as the intensity (based upon the telescope's FOV). The converse is termed a point source, in which case the strength of the signal is taken as the source's apparent magnitude for the telescope receiver's band.
Stars are generally point sources, whereas galaxies, galaxy clusters, clouds, and stellar clusters are generally extended sources, except some extremely distant examples. Within the solar system, planets are likely to be extended sources as well as comets that are near enough to be active. Minor planets may be sufficiently large and close to be extended sources or may be so small and/or distant that they are point sources.
The terms resolved source and unresolved source mean the same as extended source (implying a finite angular size) and point source, respectively.