Two-space extension

The two-space extension  

is a two-space extension along the third line, a big fuseki point which creates a base for the group and prevents Black from attacking around the same point. This is one of the most common formations in go. The two-space extension on the third line cannot be cut without the help of surrounding stones, but can be attacked in various ways; see two-space extension - unobvious answers and L'ame du go.

Fourth-line two-space extension and large knight's extension  

The Black formation on the left is also a two-space extension, but on the fourth line. The White formation is not a two-space extension, but rather a large knight's extension. Both are useful for developing groups and/or creating a base, but less stable than the two-space extension on the third line.

In the fuseki, having an option for a two space extension is an important consideration when deciding how to play inside an opponent's framework or side position.

One major consideration is whether a two-space extension has nerai, or potential for sharp follow-up moves: http://lifein19x19.com/forum/viewtopic.php?f=15&t=9491.