what determines the visibility of the laser light?

The visibility of a laser light depends on several factors. The first factor that determines visibility is the output power of the laser. The higher the output power, the higher the visibility.

 Wavelength also determines the visibility of the laser light. The human eye has a spectral response from 400 to 700nm with peak responsivity at about 550nm. So a 1mW, 635nm red laser is about 5 times brighter than a 1mW, 670nm red laser, and 3times brighter than a 650nm laser, even though they both have the same output power of 1mW.

 Lastly, ambient lighting also determines the degree of visibility. High ambient lighting levels at the target will yield low contrast and therefore low visibility.  The best visibility generally occurs in presence of low levels of ambient lighting.