Lasers create a narrow beam of light. The light is concentrated into a single, very specific frequency and color. That color can be red or green or invisible (like infrared light). And the laser creates waves of light that are the perfectly in step - imagine ocean waves, the crest of each wave exactly aligned with the crests of all the others.
Lasers in skincare use something called selective photothermolysis. That is they a target a certain color (called a chromophore) within tissue using a specific light wavelength. The laser sends out that light which creates heat and destroys the selected color target - ideally without damaging surrounding tissue.
For things like facial spider veins, the color target (chromophore) is oxyhemoglobin. It's the oxygen-carrying pigment in red blood cells that gives them their red color. For more information, read this: https://masterpieceskinrestoration.com/spider-veins-face/