A smoke precipitator, or an electrostatic precipitator, is a device which removes smoke or other particles from the air using high voltage electrostatics.
In the above diagram, the metal mesh is charged with a negative charge and the metal cylinder is charged with a positive charge.
Uncharged smoke rises up the tube. As it passes through the metal mesh, smoke particles pick up a negative electron from the mesh causing them to become negatively charged.
Unlike charges attract each other so the now negatively charged smoke particles are attracted to the positively charged cylinder and when they get there they stay there. The remaining uncharged air continues up through the tube.
The bottom edge of the cylinder is deliberately rounded/smooth. This is to avoid creating positive ions in the air and deionizing the smoke particles before they get to the cylinder. With a rounded/smooth bottom edge, the electric field there is not so strong as to do ionization.