In an n-dimensional space, an infinite n-1-dimensional thing is a hyperplane. Or put more simply: it's something that divides the space in two. In 1 dimension t

In an n-dimensional space, an infinite n-1-dimensional thing is a hyperplane. Or put more simply: it's something that divides the space in two. In 1 dimension that's a point, in 2 dimensions it's a line, in 3 dimensions it's a plane (hence the name), for more dimensions we just call it a hyperplane. Now there are various ways to define which hyperplane you speak about. The easiest to reason about is to give a couple points that are on the hyperplane (1 point defines a point, a line can be defined by any two points on that line, a plane by three points on that plane etc.). A slightly weirder but equally useful way is to say "it's orthogonal to this line, and intersects this point". That's easy to reason about in three dimensions, but apparently works in higher dimensions as well.