Audiolingualism is a language-learning theory that says that one has to engage in a lot of repetitive drills to learn a language. Specifically, these are spoken drills, where the student either repeats canned phrases/sentences or changes them in a certain way (like the verb form or tense). The teacher then provides feedback.
Audiolingualism is closely related to behaviorism, though behaviorism involves any kind of repetition (be it spoken or written) that's followed by feedback. For example, written verb conjugation drills are not audiolingualism, but they are behaviorism. Yet, if they were spoken rather than written, they would be audiolingualism.
Audiolingualism is generally not in style today, but current research says it's OK to drill from time to time, so long as the focus of the class remains on meaningful, unscripted communication. Hope that helps! I'm a language teacher and methods instructor, so let me know if you have any questions! :)