How do I show nodes/articles with specific taxonomy on a page? Maybe the title is not appropriate, so please dont hesitate to change it or give suggestions for it.

Here's how our Drupal site is done:

A vocabulary called "PAA".
With this vocabulary there are many terms organized like this:

PAA
  |
  \-- MainTerm01
  |   |
  |   \-- SubTerm01
  |   |
  |   \-- SubTerm02
  |   |
  |   ...
  |   
  \-- MainTerm02
      |
      \-- SubTerm03
      |
      \-- SubTerm04
      |
      ...


Then we have tons of articles that are associated with only one MainTermXX and only one SubTermXX (whatever XX is).
Here's what we'd like to do: make a page where we can search for a term (either MainTermXX or SubTermXX) and display all articles that are associated with the term.

My question is: is there a way to do this easily (= is this native in Drupal, just configuration) or will I have some work to do about this?
You can use Views for building the output of the page and filtering according to the search query (that is called "exposed filter" in views).

To get familiar with Views and see all what you can do with them, check out Nodeone library of videos on Vimeo.