They create artificial stars for adaptive optics.

The lasers are used to create artificial 'guide stars' in the Earth's upper atmosphere, to enable the 'adaptive optics' systems on these telescopes, a way to slightly deform the mirrors collecting light to correct for the distortions caused by the Earth's atmosphere. You can read in a bit more detail here: https://elt.eso.org/telescope/adaptiveoptics/ As they note, turbulence in the Earth's atmosphere causes the stars to twinkle in a way that "delights poets but frustrates astronomers" since it blurs the finest details.

The lasers are tuned to have a wavelength of 589.159 nm, which is the wavelength of a particular transition of Sodium. This is in the visible range, an yellowish colour as in the photo, similar to old Sodium street lamps. They excite a layer of Sodium in the upper atmosphere, which then emits light, creating an artificial 'guide star' which the telescope can then observe in order to calibrate its adaptive optics systems. These are especially useful when no real well-known source is available in the direction that needs to be observed. Having the calibrator star close to the science target is important for proper AO adjustments, as the atmosphere can be different in different directions. The lasers solve this problem because they can be pointed in pretty much any direction we want.