To see a list of them open up the Arcane section of your in-game menu. The more Soul Clusters you have the further you can develop your abilities. On the active side, this will help you develop things like your Blast, Summons, Stomp and Aura abilities, which fall into the more offensive categories. On the passive side, this means developing your Flight and Super Sprint, two essential traits to moving around the map and staying alive. The reason these Soul Clusters are important is because they are the currency used to purchase upgrades to your passive and active abilities. Unless you're in imminent danger you should always make time for Clusters. Don't be cheap here, try to gather up well over 100, and make sure to pass through any that you see when you're on your way to complete one of the game's quests.
These blue orbs are used to upgrade your abilities, and in the early parts of the game you'll want to spend a solid 10 to 15 minutes doing nothing but collecting them. One of the first game mechanics that you'll be introduced to is flight, and it's one that will allow you to gather up truck loads of Soul Clusters. You can't pick a fight with the most evil force the universe has ever known (on his turf) unless you're a lean, mean, demon killing machine.
That means you plan to go toe-to-toe with Satan, but first you're going to need to learn a few tricks and develop some of your combat skills.
If you've read our Saints Row IV: Re-Elected/Gat out of Hell review, the chances are you're either in the process of, or have just finished downloading the game.