interior point method defined in Mathworld

Question

I am studying the interior point method. However, I cannot see the whole picture so far.

As explained in the Mathworld:
http://mathworld.wolfram.com/InteriorPointMethod.html

An interior point method is a linear or nonlinear programming method (Forsgren et al. 2002) that achieves optimization by going through the middle of the solid defined by the problem rather than around its surface.

I think the interior points here means the interior of the set of feasible region (for example: the interior of the polyhedral defined by the linear programming's inequality constraints.)

I have a few questions however:

1. What does it mean "around its surface?"
2. Which method or algorithm going around the surface (hope for example, such as Newton's algorithm, ADMM....)?