Yes, in a bar magnet iron electrons are moving around atoms (and thus seen by us in "compressed" space due to relativity) thus they create a magnetic field. This field actually exists in any kind of atom, and around many atoms with non-copled electrons; but in iron and few other elements (along with some of their alloys) atomic magnetons due to interaction with each other align themselves in one predominant direction (phenomenon called ferromagnetizm). Regions where atomic magnetons alighned in the same directions are called domains. In non-magnetized iron (or alloy) domains oriented randomly minimising their total magnetic energy and you do not have a magnet yet. But if you place it in a strong external magnetic field (or rub by another magnet), you can make more and more domains aligned with this external fielg, and if you then turn the field off, some of them will not completely randomize (phenomenon called hysterizes) - and now you have a non zero average magnetic field around a piece of metal - we call such piece of metal a magnet. Some alloys "remember" more (strong neodym magnets have high hysterizis), some less (weak ferrite magnets), some almost nothing (pure or "soft" iron - like nails). Of course, you can randomize back distribution of domains orientation if you shake magnet really well (say, by repeatedly hitting it with a hammer, or by heating it red in fire, or by placing it in variable and slowly decreasing to zero magnetic field) - your permanent magnet will demagnetize (and is ready to be magnetized in any new direction by placing into strong magnetic field again).

If non-magnetized magnetically "hard" alloy rests for a long time in one position, it slightly magnetizes in Earth magnetic field (scissors, needles, screwdrivers, some TV parts, etc.) and may need demagnetisation.