Dialysis membrane is "semipermeable." It contains tiny pores that allow small molecules, such as salt, to pass through but not macromolecules such as protein. This property allows dialysis membrane to be used for "buffer exchange," to change the composition of the solution (buffer) in which a macromolecule is dissolved. The solution containing the macromolecule is placed inside the bag. The bag is then immersed in the solution into which the macromolecule is to be exchanged (the bath). The volume of the bath should be much larger than the volume of the solution inside the bag. A magnetic stirrer is used to keep the bath and the bag moving, to make sure mixing is thorough, for a period of several hours, during which the buffer exchange takes place. The solutions inside and outside the bag end up being equilibrated, consisting of a mixture of the two solutions. Since the volume of the bath was much larger than the volume of the sample inside the bag, the equilibrated solution is almost the same as the original bath solution, thus achieving buffer exchange.

MOPSO is a pH buffer. Its purpose is to maintain the pH of the solution at the desired value. DTT (dithiothreitol) is a reducing agent. Its purpose is to maintain cysteine residues in the protein in a reduced state and/or to reduce disulfide bonds in the protein. Glycerol is used as a stabilizer, to help keep the protein in its native conformation.

Why should cysteine residues be reduces? I mean reducing the disulfide bond will denature the protein and reduces it's stability?!

Some proteins contain disulfide bonds, some do not. Disulfide bonds are rarely found in cytoplasmic proteins due to the reducing environment in the cytoplasm. They are often fund in extracellular proteins because of the oxidizing extracellular environment. You probably do not want to reduce the disulfide bonds in proteins that contain them, since they stabilize the structure. However, if a protein does not contain disulfide bonds but does contain cysteine, you probably want to have a reducing agent present to keep the cysteine residues from oxidizing, which could result in intermolecular disulfide bond formation.