Electric heaters work because electric current is forced through wires that have a good deal of electrical resistance. When electric current flows through any resistance, it generates heat. Remember that moving electrons can be treated as moving waves, and the destructive interference of the atoms in the current path result in the scattering of electrons. This results in the generation of heat. All materials except superconductors have some electrical resistance.
When more elctricity is flowing through a wire than it's capapcity, the wire will get hot. This is why the larger the current, the bigger the wire you need. If you ever try to use a small extension cord to power something like a vacuum cleaner or microwave oven, you will notice that the cord gets hot.
Electric heaters work the same way. They push a lot of current through very thin specially made wires that have a lot of resistance. Hairdryers, irons, curling irons, portable heaters, toasters and toaster ovens, etc., all work like this. These devices use a lot of power, and you will often notice that using more than one on a single circuit will often trip the breaker. They have no insulation on the heater wires because the insulation would catch fire. Since the wire is bare, you can see it glow.
Incandescent light work the same way, but the wire is very, very thin so not as much power is needed to light them up and they rarely trip breakers. They average about 75 watts where a hair dryer can be 1500-2000 watts. A toaster can be up to 3000 watts sometimes.