An ionic bond is a bond that occurs between a metal and a nonmetal. The metal literally gives the electrons in its outer electron shell to the nonmetal, which is usually more than happy to accept the electrons to fill its outer shell to completion. A good example here would be FeSO4, and possibly Ti(OH)2, though the thallium would be a weaker ionic bond.
A covalent bond is a bond that occurs between two nonmetallic elements and involves the sharing of electrons between their outer electron shells. What happens here is one element loans one of its single electrons to the other element, and then on the next electron revolution, the other element reciprocates, loaning one of its electrons, along with the original electrons return to its home shell. A good example here would be carbon tetrachloride, CCl4, where the carbon has 4 single electrons in its outer shell, and each chlorine atom has room for one electron in its outer electorn shells.