In Heroes of the Storm experience is shared across the whole team making the act of gathering experience a tram effort that affects the team as a whole and not just yourself.
Experience is the way you level up, and is through leveling up that yiu get statistical attribute buffs and access to your talents. By getting more talentsyou get stronger and that strength is what makes you a more dominant and powerful hero. This is strictly linked to Game Status. By having more levels or talents than tour opponent you create an imbalance on the Game Status thus giving you advantage.

First, let's discuss where can you get your experience from:

Destroying Fortifications
Minion Waves
Mercenary Camps
Killing Heroes

1. Your first and main priority on the game is to destroy enemy fortifications. This is because you ultimately want to destroy the last fortification (The core). And alsobecause this gives you experience either trickle (forts and keeps) or static (towers).

2. Next priority are Minion Waves. Depending on the map, ~30 seconds you get 2 or 3 minion waves to collect experience from (soaking). They are the main source of your power, meaning the net difference of soaking is really important. If the kills and deaths are balanced and low (higher level games) this becomes even more important.

3. Mercenary camps also give a good amount of experience every time they spawn. They are great because they help to push the map, creating lane advantages during objectives, they help you soak minions easily and they push to destroy structures. This is not second priority because giving up a Hero to do a camp and not soak a lane is worse. The enemy gets one extra wave than your team because you lost it and they get free uncontested damage on your fortifications. The moment the camp is captured and goes in lane, it might just be quickly cleared and not get any value beyond the experience. Taking mercenary camps is an extra to soaking lanes.

4. Killing Heroes also gives a great amount of experience especially when behind. But tge higher the level the harder it is to kill freely. In order to play well you must not die, destroy buildings, soak minions and do mercenary camps. Killing only happens on an engage or if it is free. Chasing gor kills is not good, you get what they give you, and you use it to abuse the other 3 experience sources.

One of the core skills that distinguish great players from all the other ones is the ability to be consistently playing while being mindful of the game status.

There are 2 main game status: Advantage and Disadvantage. If you have a talent tier above or below your enemy team you get the Hard or Dominant distinction.

Here is how you should think:

1. Hard or Dominant Disadvantage
Your team is way much weaker than the other team. You do not have the ability to kill, control a teamfight, or contest anything. You must wait for the game status to change in order to be allowed to contest something. If your team and the enemy do not mess up, your team loses 100% of the time.

2. Soft or Weak Disadvantage
Althought you are weaker than your opponents (Level down but not Talent Tier down) you have an opportunity to win an engagement and steal your enemy's advantage to yourself. A simple and classic affirmation or example of this is to say "It's 18 vs 19, let's fight before they get 20".

3. Soft or Weak Advantage
This is the most fragile game status. You do have the advantage, but your power is not that dominant in teamfights. If you don't let your advantage go away and play macro safely then eventually you will reach a Hard Advantage and win the next game moment easily. Contest, but safely, you do have something valuable to lose, they don't.

4. Hard or Dominant Advantage
You Should and MUST do whatever you want. The map is yours now and unless you make fatal mistakes you should get away with doing anything you wish and can do. You have been playing the game to reach this point, stage or status and win. You have not reached this amount of power to stall and be afraid to lose it and never use it. By doing that eventually you make a mistake and you lose it gaining nothing and literally handing over your advantage. You have been on the other side, you know what it feels like to be under a dominant disadvantage, just do the same to them with intelligence and proactivity.