mode hopping (transverse electromagnetic mode) means that the laser is no longer producing a single dot, there are tons of TEM modes that lasers can jump to or run in, and you can find some more information here
My X105 sometimes starts out in TEM01. But after a little warmup the beams snap back together and burn the heck out of everything. Usually only happens on low batteries. It's fascinating to see two perfectly parallel beams coming out of the same aperture.
it's only a problem with DPSS lasers and most likely comes from misalignment of the crystals or defects in the crystal itself, when i was repairing my 200mw green module, slight angles to the crystals could shift it anywhere from TEM00 to TEM30
it doesn't damage the diode or really anything, it's just a non desired output
there are also longitudinal modes that arise from the size of the laser cavity. As it heats up, the cavity will expand and the mode will hop to a different one. For diodes especially, the short cavity length sometimes causes there to be multiple modes lasing at a given time because the bandwidth of the gain medium is broader than for say a gas laser which usually has a much longer cavity length.