This can be simple or complicated - depending on how you do it! For example there is a "solderiong gun" built by Wen, and Weller (two different companys)! Basically they are a step-down transformer that changes 110vac down to somewhere in the neighborhood of 6-8 volts! That is fed down to a copper tip-- I have used 8-10 gauge solid copper wire from scraps of "house wiring" When "factory tip was not near at time).. This is clamped between a couple pieces of plated (chrome or nickel), with internatl threaded copper tubing, that has a small hole drilled in each one, - a "screw with a hole in middle_ has copper wire fed through in a "loop" which is about 3" at most! The wire is inserted through the holes in the screws, and bent at 90 degrees and fed through the holes in tube,--- now the screws are tightened down till the wire is securely "jammed " tight against edges of holes in the tubing! Now the wire is bent down till it is almost 1/8 of an inch apart for a while, and there is a very sharp turn at the 100 degree bend! The reason copper is used is first of all it is cheap, - and second solder adheres very well to a cleaned- "tinned" copper tip! The copper wire will heat most and easiest at that sharp turn,- heat builds up more here because of 'kink" in wire restricting air circulation (one side is close enough to the other that is it does not cool as well here)! And second there is slightly larger distance between molecules on sharp turn outer edge (front)
so more current is flowing through a slightly smaller part of the total tip wire!

It would be very expensive to build a unit with a transformer that supplied continueous power to heat the soldering tip, plus it would burn out the tip all to often from getting too hot! ... So the "gun is equipped with a "trigger action switch", which tuns on and off power to supply transformer... This also lets tip cool off (which it does quickly to prevent burning operator, (and everythng else around that it might touch)!

The picture you show is simply a unit with a heating element that is inserted or wound around a copper "slug", which fits down in a tube to keep wires clear of touching things, and insulated so they don't touch each other,- some of these run full time, and therefore are more dangerous because of possiblilty fo burns! The nicreome is the heater, and the copper again is best thing to use for holding and heating solder & joints! making one to use directly off 110volts is possible, but has many variables in figure in out how much nicrome, and it varys betweeen thickness of nicrome, and also copper mass! Now of course could use step down transformer,- but you still have to have right ratio between resistance of heat in the element, mass of copper and of course having right temperature! And that coul d all be controlled by voltage going through the heating element!

Expirement with a "D' cell battery and a thin piece of copper wire.. like a strean form a piece of automotune wire, - or from a piece of cord from an electrical applianmce (that was broken naturally) Be cafeful here, -- bend a piece into a "U" shape, and then pinch down to a very sharp corner .. Reccomended you hold both ends of wire with pliers and touch to ends of battery (this will keep your fingers from being burned if wire way too thin for current it is carrying)! ,- if wire thin enough it will heat first at "kink", if this enough it will flash and burn off here! Basically you are working with the same principal of any "heated device" - soldering iron or otherwise!