Characters are made by taking 100 character points and using them to purchase attributes, skills, powers and other advantages; the base number of points depends on the genre in which you play and can be increased by any character by taking disadvantages. Each attribute costs a different number of character points to increase, and there is no set value for the costs of skills -- some cost a base of two, others three, and some are based on attributes and others aren't, and so on. Powers, similarly, have their own cost structures.
I don't mean to entirely denigrate the game system, however. I feel that it is more internally consistent than, say, GURPS or other generic systems, and the basic mechanics that are used in the game are kept to a minimum. During gameplay things tend to move pretty quickly once you're used to the system, or if you have a gamemaster who is used to it and can guide you.
Unfortunately, the complication of character generation makes a gamemaster's life difficult. Running a Hero System game in a fantasy setting was a goal of mine for quite some time until I finally did it and discovered how hard it was to toss together spur-of-the-moment NPCs. Yes, I know, the hardcore roleplayers will tell me that every character should be important, and that there should be no unimportant NPCs, but that isn't an attitude I agree with. If NPCs are included spontaneously in a game and a player unexpectedly chooses to interact with one, it should be extremely easy to generate (say) a bargaining skill for that character, and figure out how good they are in a fight should something awful take place. This is not so easy in Hero.
Champions is the long-lived game of four-color superheroic action described vaguely above. The game itself is actually older than The Hero System; when Champs was a success, Hero Games released the classic versions of Fantasy Hero and Justice, Inc. (a pulp-fiction RPG). Those two were not directly compatible with Champs for quite some time, though it was clear that FH's spells were like Champs's powers, and so on. Eventually at some point in the mid-to-late 80's the systems were unified.
Champions does a good job of echoing superhero comic books of all stripes; unlike Marvel Super Heroes it does not put strict moral rules into the game system; in MSH these rules make it impossible to run a character like Wolverine or Vigilante, and while I can see the reasoning behind putting them into MSH they are out of place in a more generic game like Champs.
Notable sourcebooks for Champions include Dark Champions, for the darkly-heroic games I touched on above, and The Ultimate Martial Artist, deemed by many to be the best martial-arts roleplaying supplement on the market today, and one of Hero's best sellers of recent years.
Fantasy Hero doesn't have as much source material as Champions does, due to the eternal glut of fantasy games on the RPG market, but the Fantasy Hero rulebook itself does a good job of helping a GM create a believable fantasy setting, complete with campaign theme; it also has that most-important element of a fantasy game that uses the Hero System: enormous spell lists. The Fantasy Hero Companion is also very nice, with more of the same.
Lastly, I should note that newer editions of the Champions hardcover rulebook, which include the Hero System core rules, also contain a copy of the HeroMaker software, which is a must for any serious player of the Hero System. It turns the otherwise-tedious task of character generation into something that can be done quickly and easily, and is much less intimidating for new players. I recommend it highly.