Sublimation
Sublimation occurs as molecules of a substance in the solid state go to the vapor state directly, rather than through the liquid state. There are many substances which undergo sublimation. The most common is water.
In terms of the kinetic molecular theory, we know that molecules are in constant random motion, even when the substance is below the melting point. We also know that the average speed of the molecules (kinetic energy) is directly proportional to the absolute temperature.
If the molecules are below the melting point and are kept in the solid state by relatively weak intermolecular forces (compared to the strength of the covalent bonds with in the molecule) then sometimes a molecule will have enough energy to break those intermolecular bonds and go into the vapor state.
Deposition
Deposition is a thermodynamic process a phase transition in which gas transforms into solid without passing through the liquid phase The reverse of deposition is sublimation and hence sometimes deposition is called desublimation.
One example of deposition is the process by which, in sub freezing air, water vapour changes directly to ice without first becoming a liquid. This is how snow forms in clouds, as well as how frost and hoar frost form on the ground or other surfaces.