Non-narrative is, to put it simply, the complete opposite of what a stock standard narrative is. Typically a narrative begins with a situation and then culminates into another due to cause and effect and the chase begins. With non-narrative it isn’t so simple, there are different techniques that one can use in order to create a story that doesn’t adhere to the usual narrative structures, so your three act structures or your beginning and end casual plot lines that satisfy social constructs (usually). Non-narrative tends to be more ‘art-house’ due to the main categories.
There are:
Abstract – Created around colours shaped and images.
Rhetorical – Motivated by the aim to communicate an argument and is used to direct an audience towards a particular point of view.
Categorical – Determined by arranging material in a categorical manner.
Association – In contrast with categorical form, connects material together by looking for illogical relationships.

Non-narrative can also be non-linear, meaning it may not follow a dramatic curve, the cause and effect may be back to front or they may be no plot at all. Non-narrative reminds me heavily of the theories of Bertolt Brecht. Brecht believed the main purpose of Epic Theatre was for the audience to always be aware they are watching a play, or a piece of art. Brecht believed art should make audience question aspects of their life that they wouldn’t have questioned before the performance. Non-linear non-narratives have:
Open structure – No particular form or structure
Spatial Montage – Focus from sequentially linking one shot to the other
Multi linear – A continuous flow, multiple story lines that do not follow regular linear structure

Non-narrative allows for art to be free from the normal constraints and rules that are usually tied to it. There is no wrong and right in art, only interpretation, and this is probably the most true in terms of non-narrative based art.