Nothing about this is simple (it's all "quantum" as Terry Pratchett would say. The easiest way to describe this is to start with the simplest atom, which is hydrogen with one proton and one electron (there are three isotopes with 0, 1, and 2 neutrons, but let's not worry about that here).So, let's start with two hydrogen atoms that are just wandering around...
As we said, each hydrogen atom has one proton 'P' with a positive (+ve) change and one electron 'e' with a negative (-ve) charge, so it's electrically neutral.
The thing is that atoms have energy levels, where each level can contain a certain number of electrons. The first energy level can hole 2 electrons; the next energy level can hold 8 electrons, and so on.
So, ideally each hydrogen atom would like to have two electrons to fill it's first energy level, but then it would have one proton and two electrons, so it would be electrically unbalanced. The solution is the covalent bond. In this case, when the two hydrogen atoms get close enough to each other, they start to share their electrons. The way I think of this is like two jugglers throwing balls back and forth between each other -- it all happens so fast that you can't see what's going on. The same thing happens with the atoms as illustrated below:
Because they are sharing electrons they sort of "stick" to each other and form a hydrogen molecule. Since there are two protons and two electrons, the molecule is electrically stable. And since each hydrogen atom "thinks" it now has two electrons in its first energy level/band, it's happy that way also.
In the case of helium, that has two protons and two electrons, so it's electrically stable AND its first energy level is filled, which explains why it rarely reacts with anything (hence the reason it's called a noble gas because it doesn't make friends with the commoners).
By comparison, carbon has six protons and six electrons. Do you remember that I said the first energy level holds 2 electrons and the second level holds 8. Well, in the case of carbon, 2 of its 6 electrons go to fill its first energy level, which leaves 4 in its second energy level, but it really wants 8 in its second energy level.
This explains why carbon is happy to make friends with almost any other atom. For example, it could form four covalent bonds with four hydrogen atoms to form a CH4 molecule (methane). Or each carbon atom could link with four other carbon atoms, in which case you get charcoal or graphene or diamond (depending on how you do it). Also, it explains why carbon is central to life as we know it.
I hope this helps