In quarterly college level courses that use a three digit numbering system, a freshman introductory course would be "101", a sophomore course would be "20x", junior course "30x", etc. It has since entered the lexicon to mean something at an introductory level or aimed towards beginners in a subject.
Edit: It seems colleges in the United States began to use the three-digit numbering system in the late 1920s to mid 1930s. By the 1950s it had entered popular usage
It was in use at least as early as 1929. As for when and where it became "standard", that seems hard to define. A paper from 1935 mentions it becoming a trend.
In the late 1920s. The Oxford English Dictionary finds the first use of "101" as an introductory course number in a 1929 University of Buffalo course catalog. Colleges and universities began to switch to a three-digit course-numbering system around this time. In 1935, two researchers from Kent State published a paper celebrating the efficiency of the new system: "Recently college catalogs have revealed a commendable trend toward a logical arrangement of course numbers," they wrote. "The loose hodgepodge of former years is giving way to systematic arrangement."
Slate already did some research on this subject. I don't have the citation for the actual paper they mentioned from 1935, but maybe someone else can dig it up.
Here's a New York Times article from 1957 that uses the phrase "English 101" casually as though the reader is supposed to understand the reference. It's near the end of the second paragraph:
For those who can't access the article, here's the relevant quote:
The sporadic increase of interest by stations and networks in educational television programs has given these "actors" [college professors] an opportunity to demonstrate their audience-holding power on a wider scale than meetings of English 101 can afford.