Offsetting right/left allows you to control finished dimensions on a machined part. For example, your cutting tool may wear or dull to the point where your finished part is no longer in tolerance and you can simply "offset" that tool the amount needed to cut a smaller/bigger dimension to bring the part back into tolerance.
This could be a Cad/Cam question when generating a toolpath from a drawing/model, in which case your software compensates for the radius of the tool's cutting edge.
This could also be a question regarding G41 and G42 commands in the NC program of the control, in which case the powerful math processor inside the CNC control compensates for the cutting tool's radius.
Parts with radii and radial contours can have complicated geometry and gets more complicated trying to cut these profiles with a tool that has a radius. The "offsetting" features of a CNC control and/or your Cad/Cam software tries to ease the burden of you calculating the trigonometry of the cutter toolpath verses the finished part.