Simply connected region

A region with no holes -- every loop drawn inside it can be shrunk down to a point without leaving the region.

A path-connected region is simply connected if every closed loop drawn inside it can be continuously shrunk to a point without ever leaving the region. A disk is simply connected; an annulus (a disk with a hole punched out) is not, since a loop around the hole can't shrink past it.

Examples

The whole plane, and any disk, are simply connected.
The punctured plane $\mathbb{R}^2\setminus\{(0,0)\}$ is NOT simply connected -- a loop around the missing origin can't shrink to a point.