So, when two molecules are bonding to each other they are always trying to achieve the same state, which is having a full outer shell of electrons. Ionic and Covalent bonding are two different ways of getting there. In Ionic bonding one molecule, normally with a small number of electrons in it's outer shell gives, or donates, those electrons away to another molecule with the same number of spaces for electrons in its outer shell. As electrons are negatively charged, when they move from one molecule to another, the giving or donor molecule becomes positively charged and the receiving molecule become negatively charged. Resulting in a compound which has positive and negative ions, this gives these compounds particular properties.
Covalent bonds work slightly differently. In a covalent bond two, or more, molecules will share electrons to gain a full outer shell. Because the electrons are being shared and not transferred from one molecule to another the eventual compound will have an overall neutral charge, which gives them different properties to ionic compounds.