Resource Management is important for basically everything making it a very fundamental and important skill. Managing your health, your shields, your cooldowns, ability charges and your ultimates!
But first, let's explain why managing your resources is such an important skill. It is about maintaining a balance between efficiency and effectiveness.
Let's take McCree's Flashbang for example. The cooldown isn't very long, meaning that in theory, you can use it a lot during the game. If you would use it on cooldown in a 20-minute game you could use it a total of 120 times. But you don't obviously. Noone uses their flashbang as soon as it's up, and if you die regularly you can't really use your ability in that time either. You wait for the right opportunities! Sometimes you save your flashbang to kill that pesky Tracer running behind you, and that is completely normal.
So you need to make a decision. Obviously, you want to use as many flashbangs as you can, in an ideal scenario you could use your flashbang 120 times and every time it would lead to a kill. But you also want to maximize the chances of each flashbang actually doing something. Think of your flashbang like a dice roll. If you use your flashbangs sooner you get to throw more dice in a game. But the longer you wait for each flashbang the higher the chance that it's actually going to do something. That is resource management. Trying to create as many opportunities as possible while also having a decent chance at taking those opportunities.
The crucial thing to understand is that cooldowns are a resource. You can have up to 120 cooldowns on your flashbang in a game, but only if you use it immediately. If you don't use it immediately you aren't cooling it down. Imagine if Flashbang had 120 charges. That way you wouldn't need to rush your flashbangs at all because they are recharging even if you don't use them immediately. That is why a charge system on Tracer, for example, is so strong. You don't have to use your blinks immediately, since you can have up to 3 charges. Obviously, once you have all 3 charges you aren't regenerating blinks anymore, which means that you are losing potential resources, in this case, a cooldown again.
The same thing applies to ultimates as well. Let's take Mercies old Rez. Back then her resurrect was her ultimate, and it could bring as many corpses around her back to life. So Mercy players need to make a choice. Use their rezzes as quickly as possible so that they can regenerate another one? Or should they wait until they get a lot of value?
You could hold onto your rez for very long, and that would boost your average amount of players rezzed per ultimate used by a lot. But while you hold onto your ultimate, you cannot regenerate any more ult charge. The worst case is that you hold your ult so long, that you could have charged a second one in the mean time if you had used it earlier! You need to maximize the ultimates you get, while also maximizing the value you get out of each ability.
The same thing applies to abilities like Reinhardt's Shield as well. Obviously, you want to block as much damage as possible, but that isn't always the smartest move. If you watch high-level Reinhardt players you will see that they drop their shield regularly exposing their team, because they want to make sure that their average amount of shield available gets as high as possible!
The sooner you use your abilities and ultimates, the sooner you will get them back. That is really important.
Abilities like Reinhardt's fire strike need to be maximized. Ideally on cooldown, because the chances of it hitting are very high, so holding onto it for long ends up not really being the most efficient way of generating ult charge.
Abilities like Tracers Recall or Genji's Deflect are also really important resources. Genji, for example, is a character that needs to go really deep. Imagine Genji not having his deflect. Imagine blizzard just removing that ability. You would probably play incredibly passive because you don't have that second chance button anymore. Whereas if you have your deflect available you can afford to go a lot more aggressive since if anything goes wrong, your deflect can buy you the time you need to get out. Same thing with Recall.
So the more aggressive you play, the more deflect you use each game. If you have your Deflect or Recall available you do NOT want to wait around too long. You want to maximize your pressure on the enemy team, getting behind the enemy team and drawing their attention. This way you will maximize both the effectiveness and the efficiency of your Recall.
So how do you improve you resource management?
First, use some references. Hop onto Youtube and watch the gameplay of your favorite Pro Players. Focus on 1 ability at a time. Let's take something like Zarya's bubble for example. You don't want to just spam that ability because you may end up with 0 energy gained, but you also don't want to wait too long because it will lower the amount of barriers you get to use in a single game. Watch the Pro player play and see how he handles his bubbles. How does his playstyle change once his personal barrier becomes available? Does he use his personal barrier very frequently or does he save it for quite a while until he really needs it? Try to understand the thought process behind that 1 ability. That is really important, focus on ONE ability at a time! Once you think you understand how the ability works, go in game and focus on that 1 ability. So you would go in game, pick Zarya, and keep your eyes peeled on your personal Barrier. As soon as it's up try to get into a very aggressive position and use it asap. Try to use it as often as you can without sacrificing the amount of charge you gain. If you do this for long enough it will become second nature, and you will subliminally track that cooldown and play more aggressive as soon as you get it up. Once you feel confident in that one ability, you can keep going with the other abilities. You can do the same procedure with your projected Barrier, and finally with your Ultimate.
Resource Management is incredibly important. You will NEVER have perfect resource management, but you want to get as close to 100% efficiency as possible. You want to use your abilities as often as you can while getting as much value out of them as you can. It is much better to Solo Dead Eye 5 times than get a Triple Kill with it once. The faster you use your abilities, the faster you'll get to use them again.