The style of overhead wire used by many electric railways is often referred to as catenary, because it contains a roughly catenary curve. The wire that takes this form is called the messenger wire and it is loosely hung between widely spaced suspension points. From this messenger wire hang drop wires of varying lengths connect to the contact wire which is as near smoothly horizontal as can be achieved. This is known as catenary suspension and is utilised because it allows the contact wire to be kept relatively straight and horizontal while permitting quite wide spacing of supports.
In some applications, another wire, the auxilary wire, is above and parallel to the contact wire, attached to it at regular and close intervals. The purpose of this wire is that it contains more copper than the others, allowing for better electrical conductivity. The added copper makes it softer, which would not be desirable in either the messenger wire or contact wire, for reasons of strength and wear resistance; the addition of an extra wire which is neither load bearing nor touched by the locomotives' pantographs enables better conductivity without compromise.
It has become common to refer to the whole arrangement as 'catenary', even though only the messenger wire describes a catenary curve; moreover, lazy usage has seen the term 'catenary' used to describe all overhead wire systems, even those that use no catenary curve at all!