As an acoustic phenomenon "absorption" means that any material that is struck by a sound wave does not reflect all the energy of the sound wave, but absorbs some and converts it to heat energy. Absorption applies to reverb as reverb is created by the multiple reflections of sound in a space. In any physical space, when sound is reflected to create reverb, some of the sound energy is absorbed by the walls and other objects and some is reflected, resulting in a loss of sound amplitude when reverb reflections are created.
The absorption of reverb is the loss in sound amplitude that occurs when reverb reflections are created.
You can imagine that different physical spaces reflect or absorb sound differently. You would expect, for example, that clean hard walls would reflect more of the sound compared to carpeted walls.
Thus, the absorption of reverb is just a way of characterizing how much of the sound is lost when reflected. It is the loss of amplitude in the reflections of the sound compared to the original sound. The larger the absorption, the smaller the amplitude of the reverberated sound is. The smaller the absorption, the larger the amplitude of the reverberated sound is. If, for example, a digital reverb has an "absorption" knob you should expect that when the absorption is turned to 0% all the sound is reflected back and if the knob is turned to 100% none of the sound will be reflected back and no reverb will be heard.
Since sound travels through air at practically constant speed, there is a direct relationship between the size of the room, the total length of the reverb, and the reverb absorption. In two rooms of the same size and shape the total length of the reverb (the amount of time it takes for the reverb to become inaudible) will be smaller if the absorption is higher in one of the two rooms. This means that, if you look at the controls of some digital reverbs, you may see "total length" rather than "absorption". If the digital reverb is designed similarly to the natural reverb phenomenon, "total length" and "absorption" controls should serve the same purpose.