Laurenj, if you are asking about the obverse of the coin, I will give a shot at explaining.
Historically the design of papal coins followed a sort of formula which had on their front side:
- the family coat of arms of the pope more or less in the center (historically, the popes came from noble families who had coats of arms. They don't any more). This followed a widespread European tradition of having the ruler's personal coat of arms on their coins. In its place on this coin is a disc with IHS, a sort of monogram for the name of Jesus.
- the papal tiara above, which has the same type of symbolism as a crown, since the pope is both a head of state and head of the church (there is additional symbolism to the tiara having three layers). The tiara has two pieces of cloth attached to it, called lappets, which are show here at each side (they look like ribbons)
- crossed keys tied with a cord, which symbolizes the keys to the gates of heaven.
The scene on the back of the coin is pretty self-explanatory.