[Raphaël Assénat] needed anti-static bags for some boards he is selling. He had a lot of leftovers on hand (presumably from the components he ordered to assemble these boards) and wanted to reuse them. Instead of buying a heat sealer he built his own to cut them down to size.
His build starts with a transformer to drop mains voltage down to 9 Volts. From there, you can see the two power resistors used in series to limit the current. Without these, the wire would get way too hot. Just in front of those resistors is a momentary push switch which cuts the power by default. Here we can see that [Raphaël] is using a wood block to press the bag against the wire as it heats up.
The wire itself is a piece of straightened tension spring. Apparently this spring material is a poor conductor, which is why it gets hot enough to melt the plastic bag when you run current through it.