First, I suspect you are referring to the Ramachandran plot, correct?
In contrast to all other amino acids, Gly has only a hydrogen as "side chain". Its van der Waals radius is smaller and is thus less restricted. Proline, on the other hand has a 5-membered ring as a side chain. Therefore it is much more restricted than the other amino acids and allows for only a limited number of ψ and φ.
Gly is the only amino acid that has no chiral center. Pro is the only amino acid that has a 5-membered aliphatic ring structure.
First, I suspect you are referring to the Ramachandran plot, correct?
In contrast to all other amino acids, Gly has only a hydrogen as "side chain". Its van der Waals radius is smaller and is thus less restricted. Proline, on the other hand has a 5-membered ring as a side chain. Therefore it is much more restricted than the other amino acids and allows for only a limited number of ψ and φ.
Gly is the only amino acid that has no chiral center. Pro is the only amino acid that has a 5-membered aliphatic ring structure.
In terms of looking at Gly and Pro in protein structures and how they act, you might find it useful to look at papers by Jane and David Richardson and their colleagues, e.g see http://kinemage.biochem.duke.edu/downloads/PDFs/2013Richardson_Rama50.pdf
The quick answer I always give is that they exist at the two extreme ends of the spectrum in terms of phi/psi rotation (which is what the Ramachandran plot shows). Gly is the least restricted, Pro is the most restricted. Thus Gly can appear anywhere & Pro only in certain places.
Other properties:
They are both hydrophobic amino acids - either will increase the 'greasiness' of the protein.
Naturally occurring mutations to either of these types of residues deserve special attention because there is a high likelihood that either local or global protein structure is altered when proteins undergo G->X or P->X mutations. Homology models can lose relevance when dealing with these types of changes.