The difference between ionic bonding and covalent bonding is how the electrons are distributed between two atoms.  A chemical bond arises from the fact that atoms use their valence (outermost) shell electrons to interact and bind with other atoms.  Atoms always like to have an octet (eight) of electrons in their valence shells since this is very electronically stable.  Only the noble gasses naturally have an octet of electrons in their valence shells.  Other atoms have to either take, give, or share electrons to achieve an octet.  When two atoms share electrons between each other it makes a covalent bond.  This type of chemical bond is not easily broken (in most cases).  When one atom gives an electron to another atom, this forms two ions (a positive cation and a negative anion).  These two ions share an electrostatic interaction called an ionic bond.  This type of chemical bond is often disrupted when the chemical is dissolved in a solvent like water.