The primary structure of a protein is the sequence in which the amino acids are joined. The only bonds involved in the primary structure of a protein are peptide bonds (between the amino acids).
Proteins are polymers, which essentially means that they are large molecules composed of many repeated subunits, known as monomers. In the case of the protein the monomer is an amino acid. If we imagine the primary structure as the first stage in protein formation, it is easier to understand its importance. Proteins are 3d molecules whose function is determined by its shape (whether they have enzymatic activity, carrier functions etc.). The sequence of amino acids is therefore critical to how the polypeptide chain (long chain of amino acids) will fold. This is best explained with the use of a diagram.