The character development can be combined with the equipment description as pieces of protagonist's exoskeleton are the main modifiers of his parameters. However, let's start from the beginning.
Scrap and core
The protagonist can use varied equipment. However, to do that, the exoskeleton must have enough core energy which enables it to power all the pieces (otherwise he won't be able to wear them). By killing the enemies and gathering the random loot (and by destroying equipment you don't need) you are awarded with scrap. It enables you to upgrade your core in the MedBay. New energy levels don't provide any special skills, but they allow you to overload some energy lines to open closed paths and to use more implants.
Scrap is also used to create and upgrade equipment. Because of that, it is important to wisely and skillfully distribute your resources. Notice that when you fight and defeat new opponents, the reward multiplier increases. It resets when you return to MedBay and when you use some healing methods. It can be also impacted by your implants and weapons. You should find balance between your equipment and the multiplier.
Sometimes you can also find consumables. They can provide you with various amounts of scrap. You can't do anything else with them - they are simply bonuses to consume. It is best to use them near a MedBay so that you won't lose the bonus scrap when something goes wrong.
Implants are the main thing that enable you to use new skills (mostly healing) and to use energy - the blue bar that increases during the fight (you can for example trade it for health with an implant). Some implants work passively. In addition to that, there are implants with much different effects, like showing the health bar above the enemy. You can find them like other items, usually in random places.
You can install them in free slots or uninstall them with MedBays. New slots are unlocked by developing the core of the exoskeleton. Each slot has the required level described on it.