This notion is important in mathematics and its applications, because degenerate cases may require an exceptional treatment; for example, when stating exactly certain theorems and when writing computer programs.
The most frequent use is the following.
A set of points in the d-dimensional Euclidean space is said to be in general position, if no d + 1 of them lie in a (d-1)-dimensional plane. Such set of points is also said to be affinely independent.
See the article about affine transformation for more.
In some contexts, e.g., when discussing Voronoi tesselations and Delaunay triangulations in the plane, the following definition is used.
This definition can be generalized further: one may speak of points in general position with respect to a fixed class of algebraic relations (e.g. conic sections). In algebraic geometry this kind of condition is frequently met, in that points should impose independent conditions on curves passing through them.