Anything that relates to an act, but doesn't help determine what specific type of act is done, is a circumstance. A circumstance can change without changing the type of act.
Circumstances are morally relevant when they affect how aligned the act is to the actor's final end of happiness with God.
Who, what, when, where, why, how, with what: Answer these questions, and you know all the circumstances. Fr. Walter Farrell, OP, in his wonderful A Companion to the Summa, goes as far as to say:
As a matter of fact, when we have run through these circumstances and discovered who did the thing, where it was done and why, when it was accomplished and how, and who helped, we have covered all there is to know about the event. We not only have a view of the neighbourhood, we have the whole family history and a fairly accurate prediction of the future.
If an answer to who, what, when, where, why, how, or with what does help determine the specific type of the act -- meaning that if it changed then the type of act would change -- then it's not a circumstance. Rather, it's a condition.
The most important circumstances are why an act is done and what the effect of the act is.
On the second to the last point, determining whether something is a condition or a circumstance seems to be a large part of moral theology.
On the last point, it seems to me that the why and the what meet in the object, so to speak. The object of my act is the immediate end I will; but insofar as that immediate end results in a change to the way things are before I act, it is also an effect. (This further suggests, I think, that both the why and the what at least partly touch on the formal cause.)