The ways these are usable vary by system, and really there's no right or wrongs here. The main point is to let players have a little more control over the odds from time to time. They might:
- Allow players to take an extra turn right after their current one
- Allow players to insert themselves elsewhere in the turn order
- Grant an extra die to a roll in a system that normally uses 2d6
- Add to the roll bonus
- Turn a failure into a success
- Turn a success into a critical success
- Let a character recover health
- Lessen the damage taken from a hit
- Grant additional movement points
- Allow a character to perform an action for free when it would normally take time
- Let the player define some fact about the scene or the setting that might give an advantage ("I saw an armory just down that hall--maybe we can find some weapons there!")
- Stop a player character from dying
- Allow a reroll on an action (sometimes the player can pick whichever result is better, other times the player has to take the reroll)
Many times these points are limited in some way. For instance, GURPS 4th Ed. forces the player to use character points (the same points used for upgrading) for these purposes. Other games just put a top limit on the number of points you can have at a time. Prose Descriptive Qualities's Truth and Justice variant uses an interesting system where your maximum Hero Points are equal to the amount of character upgrade points (MAX) you've earned, but aren't the same thing--meaning that you can use Hero Points freely, but if you ever upgrade your character you temporarily lessen the amount of Hero Points you can have at a time. PDQ also uses Hero Points to power certain power uses, meaning that you have to balance power use with the special advantages you think you might need.
As far as rewarding them--they're great rewards for accomplishing goals (especially secondary options), acting appropriate to the game's theme, entertaining the group, bringing the GM candy, suffering from disadvantages, or really just about anything else the GM wants. Be as generous or stingy as you feel is appropriate for your game--if you want a strongly heroic feel, pile on the points, and if you want more tension, then only give a few. Of course, there are games that shouldn't use these at all--mostly those that are intended to be bleak and fear-filled, where any step could mean a character's doom and there shouldn't be any protection from that.
I've seen these used, in some way, by: Dungeons & Dragons 4th Edition, Prose Descriptive Qualities (specifically Truth and Justice, though it may certainly be in other builds), Deathwatch, GURPS 4th Edition, Story Engine, and Savage Worlds. I'm certain other systems can be found that use it as well (and I'm equally certain that this isn't actually a completely recent development...I just haven't found it in many older systems that I've looked into.)

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