A film of oil on a puddle shows color because light reflecting off the top surface and light reflecting off the bottom surface travel different distances and arrive out of step. At some wavelengths the two waves add; at others they cancel. The film has no pigment in it at all. The color is arithmetic.
A dichroic mirror is that effect committed to, with intent. Alternating layers of high and low refractive index material, each a quarter of a wavelength thick, are deposited onto glass, typically fifty to a hundred of them. Every interface reflects a little. Choose the thicknesses correctly and at your design wavelength all hundred of those small reflections arrive in step and sum to better than 99%; a few tens of nanometers away they arrive out of step and cancel to near zero, so the light passes straight through.
This is why a dichroic can do something no colored glass can: reflect one band almost perfectly while transmitting its neighbor almost perfectly, with a transition between them only a few nanometers wide. Absorption filters throw away the light they reject and turn it into heat. A dichroic does not reject light so much as send it somewhere else, which is exactly what you want when the thing you are rejecting is your excitation beam and the thing you are keeping is a few hundred photons.