In what country/region?

/u/SweetHermitress and /u/Subs-man have addressed some of this, but hopefully I can add to the conversation and help in answering your question.

When state-funded asylums began to develop in the mid- to late-nineteenth century, the intention was "therapy"- the idea was to cure the insane and then remove them from the institution. This ideal became increasingly tempered by the reality of asylums, which in some cases in the U.S. saw a 1,000% increase in the number of long-term patients from the mid-nineteenth century to the beginning of the twentieth century. So to bring this around to your specific question, by the 1920s, curing a patient would still have been considered ideal, but by no means a necessary qualification for institutionalization.

So what was "insanity" at this time? "Disruptive" behaviour has been mentioned, and it was certainly a factor, but it was not required. Patients could be committed in a number of ways: sent from jail on the certificate of two physicians, admitted by family, or even by themselves. I'm not entirely sure of the details, but these processes remained fairly unchanged from the nineteenth century. Forms of insanity were much the same: intemperance (consistent intoxication, which could cause 'delirium'), schizophrenia, epilepsy, and other very visible disruptions. In most regards, actual mental illnesses have not changed- only their diagnoses. So if you can imagine the mental illnesses that exist today, both temporary and chronic, you will have some idea of the kinds of people who were committed. Women with post-partum depression were almost certainly committed, though not with that diagnosis. Those with visible symptoms of anxiety and depression would also find themselves in the asylum. "Mania" and "melancholy" would have still been fairly catch-all terms in the early 1920s, though developments in clinical psychiatry would soon expand the terminology used to address mental illness.

Notably, the development of "idiot asylums" at the end of the nineteenth century meant that those with autism, Down's syndrome, and other characteristics that would necessitate extra care would no longer be sent to an insane asylum (as they would have in earlier years). Their care would not be much better in the idiot asylum, however, where they might be put to work or even sterilized.

Also, being the 1920s, there would have been a new class of inmates: those with "shell shock," suffering the effects of war. Asylums received an influx of patients during and just after the First World War.

EDIT: I forgot to mention everyone's favourite cause of insanity c. 1920: masturbation. It was believed that masturbation drained young men of their vital essence and weakened them. In fact, Kellogg's corn flakes were invented by John Harvey Kellogg in order to combat masturbation-induced madness and weakness in young men.

Also, neurasthenia was a common term at the time. Ben Singer (Melodrama and Modernity) and Jackson Lears (No Place of Grace) have written on the subject extensively. Similar to the effects of masturbation, neurasthenia was a draining of the vital essences by over-stimulation.