Your gang acquires hero points by killing highly skilled gang members as described on the Gangs page.
The actual points are not displayed, rather your hero status in a specific town reflects whether or not you have points available.
When you go to a shop in a town you are a local hero in you'll see a + mark next to items you (and others with hero points) can see that no one else can see. This gives you an early chance at new or rare items.
Use 'em or Lose 'em
Hero points are "spent" in the shops of the towns where your gang is a Local Hero.
Hero points also decay over time; the townspeople are not particularly interested in the heroes of yesterday, only those of today. As a result, you may find yourself a hero one day, and just another run-of-the-mill gang the next, even though you didn't use any of your points in the town's shops.
Rare Items and Hero Points
Because hero points are used to purchase rare items it is possible that an item will become "hero only" due to non-hero shop usage.
Example: the shop has 5 Rocket Launchers that are available to all players. Someone buys 4 of them. The remaining Rocket Launcher becomes rare, and is now only available to gangs with hero points.
This means that if you have hero points and buy all of a particular item you may use your hero points even though the item did not require hero points when you made the bulk purchase.
For this reason it is recommended that you make single purchases from the shops in your "hero towns" to prevent the unintended "spending" of your hero points.
Using Hero Points to Buy Reputation
By going to My Gang and clicking the Reputation tab, you will see your reputation and if you have any hero points you will see Local Hero! (USE) next to any town you have hero points in. Unless you have a lot or are near a threshold when you use your points you will not see a chance in reputation after spending your points.
Reputation you spend hero points on by town: Somerset: Civs, Merchants, Deathrace Mafia
Rare Offroad Tyres and Other Oddities
All items have a hidden hero point value. This is the number of hero points required to purchase the item. You will only be shown hero items that are at or below the number of hero points you have. So, there may be something really cool available to others who have more hero points while all you see is a couple of Offroad Tyres and a Rifle.
Example, if you have 5 hero points and another player has 10, and a buzzer appears that is valued at 10 hero points, only the other player will see it.
This is why Rifles, and other 'mundane' items pop up first; they have the lowest hero point value.