NationMaster's encyclopedia explains Sophrosyne this way (emphasis mine):
Sophrosyne (σοφροσύνη) is a Greek philosophical term etymologically meaning 'moral sanity' and from there 'self control' or 'moderation'.
Greeks upheld the ideal of sophrosyne, which means wisdom and moderation but ultimately it's complex meaning, so important to the Ancients, is very difficult to convey in English. It is perhaps best expressed by the two most famous sayings of the oracle at Delphi: "Nothing in excess", and "Know thyself".
The term suggests a happiness obtained when one's philosophical needs are satisfied, resembling the idea of enlightenment through harmonious living. It is a nearly lost Classical ideal, but enjoying some revival today with it's emphasis on individuals to live within the proportions of reason and nature, this being achieved through wisdom and self knowledge.
The word is found in the writings of Ancient Greece, especially that of Plato in ethical discussions of the dialogue Charmides where it refers to the avoidance of excess in daily life. This term in Plato's use is connected with the Pythagorean idea of harmonia.
Professor Carl Runyon's class website has this to say (emphasis mine):
In the ancient Greek concept of divine justice (as seen in Homer), the gods punished men for lack of moderation and even more for hubris (what we might call "insubordination"). The two concepts are closely connected. The moderate man "knows his place"; the immoderate man, who lets his pride or his anger or anything else get out of hand is likely to become arrogant. This kind of forgetfulness the gods never fail to punish. The Greek word rendered as "moderation" is sophrosyne. It is one of the major clues to the Greek conception of life. What the Greeks admired was not simply moderation, but a kind of internal, self-imposed discipline that keeps the passions in check and so permits a balanced and all-around development. Emotion per se was not considered bad. It is clear that the opposites of sophrosyne is not emotion but excess. Excess of any kind is bad because it interferes with the other activities of a full, well-rounded life. Since a man or a woman who goes to excess in anything inevitably loses much, the Greeks thought that moderation is the key to the good life. Sophrosyne therefore implies order, discipline, and restraint.
All the things I've highlighted are concepts that apply to me or that I am trying to develop. Self control is high on my list of characteristics I'd like to develop. I'm not completely out of control, but I could surely improve. I love the ideas of harmonious living, wisdom, and self knowledge. Dr. Runyon's page mentioned allowing pride and anger to get out of hand. That unfortunately describes me sometimes, and I would like to improve. I felt drawn to Dr. Runyon's conclusion, that Sophrosyne implies order, discipline, and restraint. That sound kind of stifling and boring, but I think those characteristics describe me, or the person that I have the potential to be, quite well.