Here's a breakdown:
* Ionic bonds: One atom *transfers* electrons to another, creating ions (atoms with a net electrical charge). The resulting oppositely charged ions are then attracted to each other, forming the bond. Think of table salt (NaCl): sodium (Na) gives up an electron to chlorine (Cl), resulting in positively charged sodium ions (Na+) and negatively charged chloride ions (Cl-), which are attracted to each other.
* Covalent bonds: Atoms *share* electrons, creating a more stable configuration for both atoms. This sharing can be equal (nonpolar covalent) or unequal (polar covalent). Think of water (H2O): Oxygen (O) shares electrons with two hydrogen (H) atoms.
Let me know if you'd like more detail on either type of bond!