First, I will start with a canonical definition of papanca from MN 18 (translated by Ven. Sujato):
Eye consciousness arises dependent on the eye and sights. The meeting
of the three is contact. Contact is a condition for feeling. What you
feel, you perceive. What you perceive, you think about. What you think
about, you proliferate. What you proliferate about is the source from
which a person is beset by concepts of identity that emerge from the
proliferation of perceptions. This occurs with respect to sights known
by the eye in the past, future, and present.
And the same applies to the other five senses and their sense objects, including mind and thoughts.
For e.g. I see a cup. Feeling means sensing the vision of the cup with my eyes. Then I perceive it, meaning I identify it as "my late grandmother's cup" from memory. Then I proliferate, meaning I think about the times I spent with my grandmother and the times she drank using the cup. It stirs emotions about my late grandmother. Then I think about what I'm going to do with the cup in future. That's mental proliferation (papanca).
"What is Papañca?" is precisely the name of the article by Andrew Olendzki, the editor of the Insight Journal, who tries to answer this question, and then relates the purpose of vipassana later in his article, beyond my quote below.
Basically, papañca is the layers of thoughts and concepts that obscures what is barely perceived.
Imagine you walk through a canteen line and the canteen staff places five pieces of potato on your plate, while placing six pieces of potato on another person's plate. If you get angry about this, thinking perhaps, that the canteen staff is discriminating against you perhaps due to your ethnicity - well, this is an example of papañca, where it gives rise to aversion. You imagined a lot of stuff, on top of what is insignificant.
Another good example is this answer, where the author wrote that she was terrified because she misinterpreted the nightly sounds of cats mating as an adult woman and her baby crying in pain.
I've recently spoken to a depressed friend who did not feel that he is good enough and suffers from a lack of self-confidence. He cites examples of where others are better than him. I quoted qualities and examples of him that are better than each of those other persons and he was shocked. He never saw it in that way before. He was too obscured in his mental commentaries of his deficiencies that he couldn't see his good qualities and personal strengths.
But papañca can be a lot milder than that. For e.g. your feeling of patriotism or pride towards your country or ethnicity or religion is in my opinion, papañca too, as it a built-up concept.
In the article, he continues to speak of Vipassana as a means of one seeing things as they truly are.
The opposite of "papañca" could be "yathābhūtaṃ pajānāti" which means "seeing things clearly as they truly are".
From Andrew Olendzki's article, "What is Papañca?":
papahcabkirata paja nippapanca tathagata
“People delight in
proliferation, the Tathagata in nonproliferation.”
Papañca is one of those delightful Pali words that rolls off the
tongue (or bursts through the lips, in this case) and hits the nail on
the head. It points to something so immediate, so pervasive, and so
insidious that it deserves to join the English language and enter into
common usage. The exact derivation of papañca is not entirely clear,
but its sense hovers somewhere between the three nodes of 1) to spread
out or proliferate; 2) an illusion or an obsession; and 3) an obstacle
or impediment. The place where these three meanings converge in
experience is not hard to locate. Sit down with your back straight and
your legs folded around your ankles, close your eyes, and attend
carefully to your experience. What do you see? Papañca.
This term is used to describe the tendency of the mind to 1) spread
out from and elaborate upon any sense object that arises in
experience, smothering it with wave after wave of mental elaboration,
2) most of which is illusory, repetitive, and even obsessive, 3) which
effectively blocks any sort of mental calm or clarity of mind.
These are the narrative loops that play over and over in the mind, the
trains of thought pulling out of the station one after another and
taking us for a long ride down the track before we even know we’re
aboard. Bhikkhu Bodhi, eloquent as always, calls papañca “the
propensity of the worldling’s imagination to erupt in an effusion of
mental commentary that obscures the bare data of cognition” (from note
229 in Majjkima Nikaya (MN)).
Also of interest from the Tuvataka Sutta:
Seeing in what way is a monk unbound,
clinging to nothing in the world?"
"He should put an entire stop
to the root of objectification-classifications:
'I am the thinker.'
Ven. Thanissaro's footnote states:
On objectification-classifications and their role in leading to
conflict, see Sn 4.11 and the introduction to MN 18. The
perception, "I am the thinker" lies at the root of these
classifications in that it reads into the immediate present a set of
distinctions — I/not-I; being/not-being; thinker/thought;
identity/non-identity — that then can proliferate into mental and
physical conflict. The conceit inherent in this perception thus forms
a fetter on the mind. To become unbound, one must learn to examine
these distinctions — which we all take for granted — to see that they
are simply assumptions that are not inherent in experience, and that
we would be better off to be able to drop them.
That means the mind creates a self and then it objectifies and classifies everything else based on its relationship to the self.
For e.g. to a non-vegetarian, cooked meat looks like delicious food and to a vegan, it's disgusting.
The root of objectification-classification is the mental idea of the self.
The Madhupindika Sutta, cited in the question, seems to state that objectification (papañca) leads to "obsessions of passion, the obsessions of resistance, the obsessions of views, the obsessions of uncertainty, the obsessions of conceit, the obsessions of passion for becoming, & the obsessions of ignorance" and also "taking up rods & bladed weapons, of arguments, quarrels, disputes, accusations, divisive tale-bearing, & false speech".
"If, monk, with regard to the cause whereby the perceptions &
categories of objectification assail a person, there is nothing there
to relish, welcome, or remain fastened to, then that is the end of the
obsessions of passion, the obsessions of resistance, the obsessions of
views, the obsessions of uncertainty, the obsessions of conceit, the
obsessions of passion for becoming, & the obsessions of ignorance.
That is the end of taking up rods & bladed weapons, of arguments,
quarrels, disputes, accusations, divisive tale-bearing, & false
speech. That is where these evil, unskillful things cease without