Longitudinal modes in a Laser cavity Why does "lasing" occour with the longitudinal modes of the cavity, that is, why does the longitudinal modes govern the spectral properties of a laser?
 A: The spectral properties of a laser amount to the set of wavelengths the laser can emit.
Laser modes are the set of "simplest" standing-wave light fields that can exist within the laser cavity.  That set of modes depends on the shapes of the cavity mirrors and their distance apart.  Usually at least one of the mirrors is slightly concave.
Different spatial modes are modes in which the light follows different spatial paths.  For example, with two concave mirrors the light can follow an "(X)" path, always reflecting back along the path. One plane mirror and one concave mirror can support spatial modes with a "(>|" path. Unless there is a dispersive element like a grating or prism in the cavity, each spatial mode will include multiple temporal modes.
Different temporal modes are modes in which different wavelengths propagate.  A laser cavity one meter long can be filled with 1,759,779 standing wave nodes of red light having about 632.99nm wavelength, or with 1,579,778 nodes of about 633.00nm wavelength.  As long as the lasing medium will amplify both wavelengths, the laser will emit at both wavelengths.
