"I went to the theater on Saturdays when I had money."
Translation:Yo iba al teatro los sábados cuando yo tenía dinero.
"...cuando tenía dinero" could be translated as "... when I had (or used to have) money" or "... when he/she/formal you had (or used to have money". Using the second "yo" take care of the ambiguity.
The short answer is ... because you went to the theater repeatedly.
If you did something once or any other specified number of times (twice, three/four times, or during a specified period of time), use the preterite such as fui or fue.
If you did something repeatedly or habitually (such as went to the theater on multiple Saturdays during an unspecified period of time), you typically use the imperfect iba.
For those of us who are still learning the difference between the imperfect and preterite, it's probably easier to stick to the distinction (once = fui) and (habitually = iba).
However, a native speaker or advanced student can use the preterite for repeated actions in the appropriate context because they understand the nuances. According to my grammar book, you can sometimes use "the preterite to denote habitual events."
"The preterite views the event as having gone on for a finite period of time whereas the imperfect merely describes it as going on at the time or as part of the background."
"The imperfect views the habit as in progress at the time; the preterite looks back on it as an event viewed as a whole, i.e. something that continued throughout whatever period of time the speaker has in mind, e.g. his youth, those years, that period I'm talking about, etc."
However, I know that I don't understand this distinction well enough at this point to use that confidently and correctly... yet.