Paths, like layers and channels, are components of an image. When an image is saved in GIMP's native XCF file format, any paths it has are saved with it. The list of paths in an image can be viewed and operated on using the Paths dialog. You can move a path from one image to another by copying and pasting using the pop-up menu in the Paths dialog, or by dragging an icon from the Paths dialog into the destination image window.
GIMP paths belong to a mathematical type called “Bezier paths”. What this means in practical terms is that they are defined by anchors and handles. “Anchors” are points the path goes through. “Handles” define the direction of a path when it enters or leaves an anchor point: each anchor point has two handles attached to it.
Paths can be very complex. If you create them by hand using the Paths tool, they probably won't contain more than a few dozen anchor points and usually a less than that. However, if you create them by transforming a selection into a path, or by transforming text into a path, the result can easily contain hundreds or even thousands of anchor points.
A path may contain multiple components. A “component” is a part of a path whose anchor points are all connected to each other by path segments. The ability to have multiple components in paths allows you to convert them into selections having multiple disconnected parts.
Each component of a path can be either open or closed: “closed” means that the last anchor point is connected to the first anchor point. If you transform a path into a selection, any open components are automatically converted into closed components by connecting the last anchor point to the first anchor point with a straight line.
Path segments can be either straight or curved. A path is called “polygonal” if all of its segments are straight. A new path segment is always created straight; the handles for the anchor points are directly on top of the anchor points, yielding handles of zero length, which produces straight-line segments. Drag a handle away from an anchor point to cause a segment to curve.
One nice thing about paths is that they use very few resources, especially in comparison with images. Representing a path in RAM requires storing only the coordinates of its anchors and handles. Therefore, it is possible to have literally hundreds of paths in an image without causing any significant stress to your system. Even a path with thousands of segments consumes minimal resources in comparison to a typical layer or channel.
Paths can be created and manipulated using the Paths tool.