LASIK is an acronym for Laser-Assisted in situ Keratomileusis, with Keratomileusis meaning surgical improvement of the cornea's refractive capabilities, i.e. usually to overcome the defects of myopia (short-sightedness), hyperopia (long-sightedness) and astigmatism (distorted vision).
The process involves first cutting a corneal flap to allow access to the defective corneal tissue. This process involves keeping the eye open, and making an incision across the protective cornea tissue to form a flap. This is achieved via a suction ring. The flap is then lifted back (note that it is still connected to the rest of the eye). Lasers are then used to reshape the cornea tissue to remove the defects. The flap is pulled back over the cornea tissue and left to heal.
The laser used operates using rapid pulses of low-energy-level ultraviolet light. The are other forms of eye surgery other than LASIK, but they depend more on the patients individual eye issues.
This video from the U.S. Food and Drug Administration shows the processes involved.