What is “obstruction of justice” and why is it such a big deal?

IANAL, as I'd often read on electronic bulletin-board systems, but I was curious about the so-called Mueller Report, officially titled Report On The Investigation Into Russion Interference In The 2016 Presidential Election (here's a link to a PDF of the redacted version).

Volume II of the Report “addresses the President’s actions toward the FBI’s investigation into Russia’s interference in the 2016 presedential election and related matters, and his actions towards the Special Counsel’s investigation.” (p. 3, or page 11 of 448 in the PDF). It begins with some terms of reference, or rules of engagement, which I’ll summarize here. In this list, when I write “they” or “their” I refer to the office of the special counsel, i.e., Mueller’s team.

• “First… we determined not to make a traditional prosecutorial judgment.”

  A traditional decision means they’d decide to either prosecute or decline to do so. Because the Office of Legal Counsel (OLC) said that you can’t indict or criminally prosecute a sitting President, they avoided that traditional decision process.

• “Second…the OLC opinion…recognizes that a criminal investigation during a President’s term is permissible.”

  Also the OLC opinion says a President’s immunity from prosecution doesn’t extend beyond his term. Therefore they “conducted a thorough factual investigation in order to preserve the evidence when memories were fresh and documentary materials were available.” Does this sound to you like Mueller is anticipating criminal prosecution later?

• “Third,” they avoided “an approach that could potentially result in a judgment that the President committed crimes.… Fairness concerns counseled against potentially reaching that judgment when no charges can be brought.”

  If you can’t charge someone, it’s unfair to them to say “we would file charges if we could” because that person has no chance to clear themselves at trial.

• “Fourth, if we had confidence… that the President clearly did not commit obstruction of justice, we would so state. …[H]owever, we are unable to reach that judgment.”

  They can’t conclude that he committed obstruction of justice because they avoided an approach that could potentially result in such a conclusion. They can’t conclude that he did not commit a crime “[b]ased on the facts and the applicable legal standards.”

I hope you consider whether Barr’s “not a summary” fairly represented the 1^st and 3^rd points above.

The Report also provides a surprisingly readable introduction to what “obstruction of justice” means. The summary, which begins on page 9 of Volume II (page 221 of 448 if you're reading the redacted PDF), outlines three basic elements

1. Obstructive act.
   which includes conduct that could obstruct or impede the administration of justice;
2. Nexus to a pending or contemplated official proceeding.
   meaning a connection to a judicial or grand jury proceeding (1503) or a pending federal agency proceeding or a congressional inquiry or investigation (1505). The proceeding need not be in progress; it can be “contemplated” (1512).

   The obstructive act has to be likely to obstruct justice in the proceeding, inquiry, or investigation in question.

3. Corrupt intent
   here meaning an intent to obstruct justice knowingly and dishonestly, or with improper motive.

With all that, why would it be a big deal if the President did in fact do things that would likely impede or obstruct the administration of justice in a pending or in-progress or soon-to-start proceeding or investigation, and did so knowingly and dishonestly, or with improper motive?

I’ll leave the answer as an exercise for the reader :-(