Tents are described being either single or double wall.
What is the difference and when is one preferred over the other?
The difference between a single wall tent and a double wall tent is the rain fly (or lack thereof). A single wall tent has only one layer of fabric, this layer provides protection from the elements, and is the only walls of the tent. A double wall tent usually has a mesh inner tent with a fly that sits on top to protect you from the elements.
The benefits to the single wall tent are it's lightness (because there are fewer parts) and it's price (again fewer parts means cheaper tent). The downsides of a single wall tent are that ventilation can be poor causing condensation to build up in the tent. That brings us to the double wall tent, it's primary benefit is keeping condensation from building up. (Newer double wall tents have mitigated the heaviness of the additional fabrics by using newer materials that are pretty light.)
For more information this article was pretty helpful.
Double wall tents keep most of the condensation from forming on the inside of a tent, and they're warmer. In general, they do a better job keeping the rain out. Double wall tents are preferable in colder or rainy weather, and I consider them a necessity for snow camping.