The term point source generally means an observed astronomical object that focuses as a point or an Airy disk as opposed to a 2D image of the object, such as showing a spherical object as a disk. The converse is a resolved source or extended source. Whether an object is a resolved source depends upon the resolving power (angular resolution) of the telescope used to observe it: in general, the larger the telescope's aperture, the better its angular resolution. It also depends upon wavelength, given a telescope, the shorter the wavelength, the smaller angle can be resolved.
For the human eye, stars are point sources and the Sun and Moon are resolved sources. Visible planets are near the line: good eyesight can barely resolve Venus at its closest. Stars are generally point sources even for telescopes, though a few nearby giant stars can be resolved using the best possible angular resolution, i.e., interferometry. Many minor planets are too distant and small to resolve. Nebulae and galaxies and stellar clusters can be resolved if not too distant. To some extent, it is point sources that scintillate (twinkle), but planets visible to the naked eye tend not to do so, but aren't quite resolved.
The term point source also is used in another way within astrophysics, as a source of EMR (or something else) that is a mathematical point. This might be called a "true point source", and the above an "apparent point source", which has that appearance because of distance. Such a "true point source" is an ideal, used in models to approximate something that is of negligible size relative to the phenomena of interest. Within such a model, EMR is spreading out from the given mathematical point, whereas with the term's use as a very distant actual object (per above), EMR being received is virtually parallel, i.e., any such spread is negligible.