I believe the answer is facilitated diffusion. :) The binding of the substance selectively to a membrane-spanning protein changes the 3D conformation and charge of the protein, such that the protein projects the substances towards the other side of the membrane down a concentration gradient.
'Hydro'means water and 'lysis' means to break. Hydrolysis is the process of breaking a compound by using water as seen in the diagram above where a peptide bond is being broken between two amino acids.