When a liquid or solid evaporates, it turns into a gas. In a closed container, pressure builds as gas accumulates.
There are two competing processes. In the solid or liquid, the higher energy atoms at the surface fly off. In the gas, the slower atoms stick to the surface and condense. The number of atoms available to condense is proportional to the gas pressure. The vapor pressure is the pressure at which to two processes balance.
Vapor pressure is temperature dependent and material dependent. Yes, a high vapor pressure means faster evaporation.
Sputtering is done under high vacuum. A material is heated until atoms fly off. They fly in a straight line to a target or the walls of the vacuum chamber, where they stick.
Flying in a straight line means they arrive with the same energy as they left (gravity can be ignored). Atoms in a substance have a range of energies. Only the most energetic ones fly off. They are much more energetic that the average atom at the temperature of the target or even the heated substance being sputtered. If a gas was in the chamber sputtered atoms atoms would strike other atoms and cool off. A high vacuum is important.
Also many applications of sputtering require very a high purity. Any residual gas in the chamber can become an impurity.
Molecules like water are "sticky." When a vacuum chamber is pumped down, there is still a layer of water on all surfaces. This will slowly evaporate and spoil a good vacuum. To get rid of it, a vacuum chamber is often heated until the water bakes off and is pumped out.
Materials like lead or zinc have a higher vapor pressure than iron. If a vacuum chamber contains these, they will contaminate the chamber.