An ionic bond is formed by the complete transfer of some electrons from one atom to another. The atom losing one or more electrons becomes a cation or a positively charged ion. The atom gaining one or more electrons becomes an anion which is a negatively charged ion.
The bond that holds together the two amino acids is a peptide bond, or a covalent chemical bond between two compounds (in this case, two amino acids). It occurs when the carboxylic group of one molecule reacts with the amino group of the other molecule, linking the two molecules and releasing a water molecule.