Ionic and covalent bonds are the two extremes of bonding. Polar covalent is the intermediate type of bonding between the two extremes. Some ionic bonds contain covalent characteristics and some covalent bonds are partially ionic.
In Ionic bonding, the atoms are bound by the attraction of oppositely charged ions. Table salt is the example of an ionic bond. Sodium and chlorine ions come together to form sodium chloride or NaCl. Whereas, in covalent bonding, atoms are bound by sharing electrons to attain stable electron configuration. Carbon dioxide (CO2) is the example of a covalent bond. One carbon atom joins with two oxygen atoms. But it has shown that substances with standard covalent bonds seem to be weaker than those with ionic bonds because the ionic bond tends to form a lattice structure, that makes them much stronger. You can see the fact that the boiling point of table salts are much higher than that of covalent like carbon dioxide.
Both of these bonds are important in organic chemistry. Ionic bonds are important because they allow the synthesis of specific organic compounds. Scientists can manipulate ionic properties to form desired products. Whereas, covalent bonds are important since most of the carbon molecules interact primarily through covalent bonding. Covalent bonding allows molecules to share electrons with other molecules, creating long chains of a compound and allowing more complexity in life.