Sublimation is the process of a solid going straight to a gas. As another answer stated, this can be seen with dry ice. When dry ice 'melts' it just creates a fog and turns back into the gaseous state of carbon dioxide. Sublimation is a change in the state of matter, just like melting, freezing, and evaporation.
It can be looked at as such: a solid that has a very low melting point, it won't melt, but it will immediately 'boil' and evaporate. The process would be similar if you had a super stove that could boil and evaporate water at a moment's notice.
The change in state from a solid directly to a gas is called sublimation. An example is called frozen carbon dioxide which changes instantly into gaseous carbon dioxide without going through a liquid phase. For example, "dry ice" is frozen carbon dioxide.
Whether a solid changes directly to gas or first to a liquid, then to a gas depends upon the pressure. Sublime substances are not common. Examples are iodine, which does not go through a liquid when changing phases. Carbon dioxide is another example. It does not go through liquid during this process either.