Offsetting a path means expanding or contracting it in such a way that each point moves perpendicular to the path in that point. Offsetting inward is called insetting, and offsetting outward is called outsetting. Imagine that your path is an island; then, outsetting means enlarging it by moving every point of the shoreline the same number of steps seaward, and insetting makes it smaller by allowing the sea to encroach inland by the same number of steps everywhere:
To inset the selected path or paths, press either 
(inset by 2 px), or 
(inset by 1 screen pixel at the current zoom), or 
(inset by 10 screen pixels). To outset a path, use the 
key with the same modifiers. On most keyboards, the 
and 
are on the same keys as 
and , so the digits will work the same as the parentheses.
Offsetting is used in situations where you want to make a path “bolder” or “thinner” without changing its overall shape. This is useful for shadows, outlines, halos, bevels, and the like. (Sometimes, instead of outsetting you can simply set a wide enough stroke on the path, colored the same as its fill.)
If you outset and inset a path several times, it becomes distorted in a characteristic way, similar but distinct from the distortion of simplification (12.3 Simplifying). Such distortion welds together parts of a path, rounding corners, smoothing the intersections, and fusing together close brush strokes within a path. For example, try to union all brush strokes of a drawing, and do a few inset/outset cycles on it to make it appear more natural and worn-down, as shown in Figure 12-15.
Offsetting, just like simplification, is a destructive operation: You cannot restore the exact original path except by undoing it. (For one thing, offsetting an open path always closes it.) However, Inkscape also has two dynamic object types, linked offset and dynamic offset, which store the exact original path and let you adjust the amount of offsetting without accumulating distortion (13.2 Dynamic and Linked Offsets).
Also, while the Inset and Outset commands apply the same offset distance to the entire path, it is also possible to inset or outset just one part of a path (for example, one tip of a calligraphic brush stroke) using the Grow and Shrink modes of the Tweak tool (12.6.4 Shrink/Grow Mode).