In NURBS curves and surfaces, fusing connects a point to a point or a CV to a CV. (You can't fuse a CV to a point, or vice versa.) This is one way to connect two curves or surfaces. It is also a way to change the shape of curves and surfaces.
Fused points behave as a single point or CV until you unfuse them. Fusing points does not combine the two point objects or CV sub-objects. They are connected but remain distinct sub-objects that you can unfuse later.
Fused CVs behave much like a single point, but the property of multiplicity for coincident CVs also applies. The fused CVs have proportionally more influence on the curve, which can become more sharply curved in the fused CVs' vicinity, or even angular if more than two CVs are fused together. See Editing Curve CV Sub-Objects.