Mostly general purpose laser pointers are used for pointing things at smaller distances eg. Diagram or Equations in Powerpoint presentations, so the power of such laser pointers is quite limited/restricted to 5mw ( Class 3A or IIIa) or 10mW in some regions.
Because of the low power and small aperture of laser pointers if you point them through empty space, you can only see them impact spot where it hits a surface.

So to point stars/planets as in astronomy club during observation sessions these low power laser pointers are not useful as there is no surface where the beam can hit & you can see the spot.

Some higher-powered laser pointers project a visible beam via scattering from dust particles or water droplets along the beam path.
Higher-power ( Class 3B or IIIb lasers: greater than 5mW) and higher-frequency (Green or Blue) lasers may produce a beam visible even in clean air because of "Rayleigh Scattering" from air molecules, especially when viewed in moderately-to-dimly lit conditions. The strong wavelength dependence of the scattering (~λ^ −4 ) means that shorter (green & blue) wavelengths are scattered more strongly than longer (red) wavelengths.

[ Rayleigh scattering is the mainly the elastic scattering (in lay term collision) of light or other electromagnetic radiation by particles much smaller than the wavelength of the light.
Rayleigh scattering results from the electric polarizability of the particles (locally separating positive & negative charges by small distance apart inside the atom. i.e. temporarily separating centre of positive charge and centre of negative charge). The oscillating electric field of a light wave acts on the charges within a particle, causing them to move at the same frequency (hence the green colour). The particle therefore becomes a small radiating dipole (or small sources of light) whose radiation we see as scattered light (the beam passing from pointer to star pointed). ]

The intensity of such scattering increases when these beams are viewed from angles near the beam axis. (That's the reason, if you are standing close to the person pointing stars in astronomy club, you can see the beam bright and clearly whereas the people standing away can barely see it. So always stand near the presenter But avoid contact with your eye. :-) )

The apparent brightness of a spot from a laser beam depends on the optical power of the laser, the reflectivity of the surface, and the chromatic response of the human eye. For the same optical power, Green Laser light will seem brighter than other colours because the human eye is most sensitive at low light levels in the green region of the spectrum (wavelength 520–570 nm). The most sensitive pigment, rhodopsin, has a peak response at 500 nm. Sensitivity decreases for redder or bluer wavelengths.

Further, Green laser pointers are of moderate power (sufficient for Rayleigh Scattering in clean air), they are compact and relatively cheaper than blue ones (even though human eye is less sensitive to blue colour, blue laser are a little bit more expensive than green one.)

Avoid their contact with your eyes and don't point them at aircraft.
People have been given up to five years in jail for aiming a green laser at an aircraft.