Formation of atoms question Could you please, explain to me the logic of the folllowing process as you would do to your 8 y/o sister:

Ubiquitousness and stability of atoms relies on their binding energy,
  which means that an atom has a lower energy than an unbound system of
  the nucleus and electrons. Where the temperature is much higher than
  ionization potential, the matter exists in the form of plasma – a gas
  of positively-charged ions and electrons. When the temperature drops
  below the ionization potential, atoms become statistically favorable.

Source: wiki
How that that binding energy can be explained in plain English? Is it somewhat intrinsic to atoms, with each kind having its own level of binding energy? I understand that this can be translated in the language of closed systems using terms as Gibbs energy (G), etc. - but how? Can the same process be describes as a kind of abstract thermodynamic system? I mean atom is a closed system, it reveives (some absctract) energy, etc. Can the same break up/formation of atoms be explained in terms of intrinsic energy potentials (i.e. systems linguo)? 
 A: This answer describes the quoted text for "8 year-old sisters;" 8 year-old brothers might also get it too. I do not address the inquiry about systems & thermodynamics.

Ubiquitousness and stability of atoms relies on their binding energy, which means that an atom has a lower energy than an unbound system of the nucleus and electrons. 

Atoms make up everything you see around you.
Atoms themselves are made of two types of charge: positive and negative. 
It so happens that opposite charges attract. 
This is why atoms tend to stay together.
Now, since they attract, it takes some effort/energy to separate the constituents.
The amount of energy needed to separate them is called the "binding energy."

Where the temperature is much higher than ionization potential, the matter exists in the form of plasma – a gas of positively-charged ions and electrons.

Imagine that a bunch of atoms are put somewhere very hot, like an oven.
When things are hot, they move around back and forth very quickly. 
Now focus on just one atom.
This atom will eventually be hit by one of the other fast-moving atoms.
If the temperature is set high enough, meaning the atoms are moving around fast enough, then during the collision enough energy is given to the atom to break up some of charges that make up that atom.
This process of some of the charges breaking up is called ionization.
Back to the hot oven. 
Since we have a bunch of atoms that are all hot, you'll have a bunch of negative and positive charges floating around.
This is called a plasma.
(Some people call it a fourth state of matter, in addition to solid, liquid, and gas.)
In a plasma, the two types charges are actually still attracted to each other, but they can't stay together because if they try, they'll just get bumped again by the other hot stuff.

When the temperature drops below the ionization potential, atoms become statistically favorable.

But once things cool down again, the attraction of the opposite charges will cause the atoms to recombine and stay attached.
