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 The subjunctive usually appears in sentences where the speaker intends for the action to be understood as a wish or simply an idea. Sometimes, however, the nonfactual “feel” that the subjunctive mood provides is used for something else. The subjunctive mood can also push an action into the background so that the action illustrated by the main verb (i.e., the verb in the indicative mood) can be made more vivid. This is what cum clauses do.

 There are four different ways to read them. Three of those ways use a verb in the subjunctive mood; the other one is indicative.  cum temporal clause: Cum adv ē nit, laet ī er ā mus. (When he arrived, we were happy.)  cum circumstantial clause: Cum adven ī ret, laet ī er ā mus. (When he arrived, we were happy.)  cum causal clause: Cum adven ī ret, laet ī er ā mus. (Because/Since he arrived, we were happy.)  cum concessive clause: Cum adven ī ret, laet ī tamen er ā mus. (Even though/although he arrived, we were happy [anyway].)

 Cum temporal and cum circumstantial clauses translate the same way (“when …”), but they use different moods because they emphasize different things.  Temporal clauses put their verbs in the indicative. They stress the time the main clause took place. (The word “temporal” comes from the Latin tempus, temporis: time)  Circumstantial clauses have verbs in the subjunctive. They show the circumstances under which the main clause takes place. By using the subjunctive instead of the indicative, they downplay the importance of their clauses, which in turn emphasizes the main clause.

 Cum causal clauses do exactly what their name suggests.  They show the cause or reason for whatever the main clause says.  The subjunctive stresses the possibility of cause rather than the fact of the matter.

 Cum concessive clauses aren't very common, but they are easily recognized by the inclusion of the word tamen (“but, anyway, nevertheless”) in the main clause.  Another way to translate the above example could be: “He arrived, but we were happy anyway.”  The cum clause sets up the circumstances, but it's the tamen in the main clause that provides the gist of the entire sentence.

 So, when you're reading, how do you know which kind of cum clause it is? If it's temporal, the verb will be in the indicative mood. If tamen appears in the main clause, it's concessive. That leaves circumstantial and causal. To tell them apart you need to rely on context.

The conjunction cum is not the same as the preposition cum meaning “with.” They are totally different words. The conjunction was quom in archaic Latin. That it evolved to look like the preposition is a coincidence. If you see the word cum followed by an ablative, you've got the preposition. If cum starts a clause that has a verb in the subjunctive (as they usually do), then it's the cum we just discussed.