Michael:

Here's a good joke, never trust an atom because they make up everything.  It's funny 'cause it's true!  Not that atoms are untrustworthy, but that everything is made of atoms.  And they're only able to make up everything because they bond, forming molecules.  But, what makes the atoms come together?  And once they're together, what makes them stick?

Well, atoms can be kinda promiscuous.

The basic structure of an atom is a nucleus, which is made of positively charged protons and electrically neutral neutrons, all orbited by negative electrons.  But most specifically, electrons are attracted to protons because positive and negative charges attract each other.  This, along with other forces, keeps electrons mingling at various distances around the nucleus in what we call electron shells.

But at just the right distance and energy level, the outermost electrons in these shells may become attracted to the nucleus of another atom as well.

Hey, I mean, this just happens sometimes.  No need to feel bad for the first atom.

Because, when this occurs, the two atoms can get so close that their electron shells overlap and the electrons are essentially shared by both atoms.  This is a chemical bond.

All chemical bonds work like this, but bonds between different kinds of atoms have different characteristics depending on the level of attraction that's going on among the electrons and the respective nuclei.

The force with which an atom attracts electrons is called its electronegativity and if a highly electronegative atom bonds with a less attractive one, the shared electrons will tend to hang out closer to the more electronegative atom.

And if the difference between the two atoms' electronegativity is really big, then the shared electrons will end up being so much closer to the attractive atom that we often consider them to be transferred to that atom, lost by the other one.

This is an ionic bond, and it sounds kinds of unfair but saying that the electrons left one atom and were transferred to another is really an oversimplification.  In reality the electrons aren't actually transferred, it's more accurate to say they are very, very unequally shared.

Now if atoms have about the same electronegativity, the electrons they share spend roughly equal amounts of time near each nucleus.  We call this a covalent bond, and it's a much more equitable relationship for both atoms involved.

So in the end, the way atoms bond and the way we distinguish between different bonds all comes down to attraction.

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