Resource management is about collecting, monitoring, and leveraging quantitative resources with incomplete information. Any game with complex resource management, that offers compelling choices, will involve imperfect decisions, leading to interesting strategy.
In simple English, this means you get money, ore, pylons, or whatever counter, and this has to be used wisely to compete. You never have enough information to make fully informed decisions, and must develop the best strategy you can with imperfect information. This mechanic is prevalent in games of almost every genre. In video games, you can see this as economies (EVE Online), resource gathering (many RTS, such as Command and Conquer), Auctions (many MMOs such as World of Warcraft), and even in ammo management and health in first person shooters, such as Quake or Doom.
Having a visible, quantitative counter of how much of a given resource is available can cause psychological stress and also satisfaction given different conditions. For example, a health bar is directly tied to a loss state in a game. Watching the health bar deplete will cause stress on the player, perhaps causing them to rethink their decision to run headlong into a room of enemies that they otherwise - at full health - wouldn't have blinked at. This stress state can be useful when trying to slow the pace of gameplay and force a more cerebral strategy. Be careful that this is not applied heavy handed, otherwise it can frustrate a player.