The MHC class-I pathway supports the detection of cancer and viruses by the immune system. It presents parts of proteins (peptides) from inside a cell on its membrane surface enabling visiting immune cells that detect non-self peptides to terminate the cell. The ability to predict whether a peptide will get presented on MHC Class I molecules helps in designing vaccines so they can activate the immune system to destroy the invading disease protein. We designed a prediction model using a BERT-based architecture (ImmunoBERT) that takes as input a peptide and its surrounding regions (N and C-terminals) along with a set of MHC-I molecules. We present a novel application of well known interpretability techniques, SHAP and LIME, to this domain and we use these results along with 3D structure visualizations and amino acid frequencies to understand and identify the most influential parts of the input amino acid sequences contributing to the output. In particular, we find that amino acids close to the peptides' N- and C-terminals are highly relevant. Additionally, some positions within the MHC proteins (in particular in the A, B and F pockets) are often assigned a high importance ranking - which confirms biological studies and the distances in the structure visualizations.