Yep this is "magnet wire"
It indeed needs a soldering iron set to 400°C or more to melt away the thin coating of insulation. This works well for making bodge wires on PCBs since it is commonly available in very thin diameters and the insulation coating takes up almost no space, so you can solder it onto tiny components like 0402 passives or 0.4mm pitch chips nicely. It also blends into the PCB pretty well, making the bodge less visible.
Some flux also helps eat away the insulation, so i will usually tin the end of it on a hot soldering iron by adding some solder to it. There is so little insulation material that it doesn't really make any mess. Scraping it off on such thin wire is way too fiddly and time consuming. It is designed to be simply soldered at high heat, that's how tiny transformers, relay coils etc... are terminated, first wrapped around a post then soldered.
Tho personalty i tend to use Kynar/PVDF wire for this. The wire i got is also often tin or silver plated, making it easy to solder without tinning. The insulation is a bit bulkier, but has a nice property of shrinking slightly when exposed to soldering iron heat, yet not melting. So you can just cut it to length then press the soldering iron against the end to make the insulation shrink away and expose about half a milimeter of wire for you to solder onto a IC pin.
If you want jumper wires for breadboard use, just cut up a solid wire CAT5 ethernet cable. Those are the perfect size for breadboards and you get lots of colors.