So, a fungible resource is one that can be easily replaced with another resource of the same kind. If you have a cup of water, and pour it into a bucket of water, then scoop out a cup, you're pretty much where you started. Ditto something like a twenty dollar bill or a couple volts of electricity. There are all sorts of interesting economic implications to resources like this (in contrast to distinct one) but they're also useful to think about in game terms.
A lot of the numeric values you see on a character sheet are fungible. Things like attack bonus or hit points are made up of an aggregate of other numbers (Stat bonuses, equipment bonuses, level and so on) and while those elements may matter a great deal when you're building the character they all run together once the dice hit the table. If you hit that enemy, there's nothing in the flat bonus that tells you whether you hit him because you're strong, because your weapon is particularly accurate or because of the advantage you got from flanking the guy.
This means that, in practice, bonuses are interchangeable. There are few places this is more evident than in 4e, where different stats often end up being used for the same thing (such as making attack rolls). here are a lot of benefits to this approach. It's incredibly flexible. Adding new elements requires only that they fit into the current economy, so swapping out parts is easy. It all comes out in the wash when it comes time to calculate the final total. It also makes (as 4e illustrates) reskinning of elements entirely trivial.
But all of this gets interesting when you contrast it with elements of the game which are very clearly not fungible. To stick with the D&D example, if you miss an attack, but then use an ability that grants you a reroll and hit, your sense is that you hit because of the reroll. If the power had given you an extra bonus before you rolled, you probably would not think "I hit because of this power" because it's just one of many factors in your total bonus, but since the reroll is a change of type (from a fungible resource to a distinct one) then that's where the cool thing happened.
You get similar reactions when you look at the results of attacks. More damage is nice, but since damage is fungible, it's not particularly cool if your damage came from hurling daggers of pure ice and my damage came from hitting the guy with a very big stick. Things get more interesting when there is differentiation in the form of non-fungible elements like extra effects. If my ice daggers slow a guy down and your big stick knocks him back then our attacks now feel different in a way that pure damage didn't allow.
This is an incredibly important point to understand when you start thinking about the role of color in an RPG. Some systems are almost entirely fungible, with the understanding that all distinctions in effect are part of the color. Other games have very limited fungible elements and lots and lots of unique elements. But it's not a simple split. On one level, everything in Hero is fungible - the underlying idea of what a point is worth is the currency everything can be broken down into, but the complexity in doing so creates a barrier to treating it as truly liquid. And more, there's no 'right' way to handle it. More or less fungibility does not make a system better or worse.
But it can make a system more or less in keeping with your vision, and suggest where you need to put in levers. To use the previous combat example, you need to decide if pure damage is enough to handle things in your system or if you need points of distinction. You can decide if general bonuses get you what you want, or if you need make things a little more specific.
Again, do with it what you will, but if you stop and look at a part of your system and ask what this looks like if you swap in something else, and if that's what you want to see. 4e shows us how useful it can be, but also demonstrates that doing it well requires really committing to the idea. If you're not willing to go that far, then make sure you're getting what you're hoping to find.
1 - I am using this word in a way that will make strict economists cry, but it's a useful concept, so if you are enough of an economist to get where I'm taking artistic license, please accept it as that.
2 - yeah, theoretically rerolls could be fungible too, but at least in 4e. In fact, by standardizing things, most of the element sin 4e are fungible - a "stunned" status works the same whether it's from a blow to the head or from a painting of the 8th dimension. This is intentional, since it allows for easy swapping of color without disrupting mechanics. That said, rerolls are player-controlled and serial, so they're different enough to be a useful example.
3 - And this one's for the nerds - Liquidity is NOT fungibility. Liquidity is the ability to turn something into something's intrinsic value into actual value. A golden statue may be worth a lot, but it's hard to spend, so it's illiquid. Sell it for cash ('liquidate' it) and now you've got some money to burn, but while that money may be fungible, that doesn't mean the statue itself is. Fungible and Liquid often get conflated if only because liquidating something usually means exchanging it for a fungible asset (since they're more easily exchanged).
4 - The Ironclaw/Jadeclaw system does something interesting with this. You roll several dice when you act, one for stat, one for skill and so on, with each bonus expressed as a die. You pick the high roll and based on which die it is, you know why you succeeded (and can infer color about other things from the roll too). Cortex could also support this too, but it does require some curious bookkeeping when rolling more than one die of the same type - you'd need different color dice and some clear way of distinguishing them. Kind of a pain, but very neat in theory.