With emacs, how to go to the pairing (balancing) parentheses

Use C-M-right and C-M-left (respectively backward-sexp and forward-sexp) to go to the beginning or the end of the current expression. This works for parenthesis pairs but also for plain words.

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As mentioned in emacs wiki (http://www.emacswiki.org/emacs/NavigatingParentheses):

C-M-n forward-list Move forward over a parenthetical group

C-M-p backward-list Move backward over a parenthetical group

C-M-f forward-sexp Move forward over a balanced expression

C-M-b backward-sexp Move backward over a balanced expression

C-M-k kill-sexp Kill balanced expression forward

C-M-SPC mark-sexp Put the mark at the end of the sexp.

https://superuser.com/questions/677516/how-do-i-jump-to-the-opening-or-closing-paren-brace-in-emacs

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For parentheses, braces and brackets just double clicking on them does the trick.

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I suggest C-M-f and C-M-b, as C-M-right/left are already bound to my DE (switch to desktop on the right / left).

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I use the following small function for exactly that (though I don't know whether or not it matches vim's behavior; I'm no vim user myself):

(defun mo-match-paren (arg)
  "Go to the matching parenthesis."
  (interactive "p")
  (cond ((looking-at "\\s\(") (forward-list 1) (backward-char 1))
        ((looking-at "\\s\)") (forward-char 1) (backward-list 1))
        (t (self-insert-command (or arg 1)))))

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I would highly recommend SmartParens it has extensive navigation and manipulation of parenthetical structures (ie. wrapping, quotes, tags, brackets, braces, regular parentheses, sexp, etc.) With support for many languages, and structures, with easy customization.

It also supports fairly complex structures, which are referred to as hybrid-s-expressions in it's documentation. Which makes it extremely powerful for manipulating code in languages such as C/C++, Java, JS etc.

For navigation the following are used.

sp-forward-sexp (&optional arg)                 ;; C-M-f
sp-backward-sexp (&optional arg)                ;; C-M-b
sp-down-sexp (&optional arg)                    ;; C-M-d
sp-backward-down-sexp (&optional arg)           ;; C-M-a
sp-up-sexp (&optional arg)                      ;; C-M-e
sp-backward-up-sexp (&optional arg)             ;; C-M-u
sp-next-sexp (&optional arg)                    ;; C-M-n
sp-previous-sexp (&optional arg)                ;; C-M-p
sp-beginning-of-sexp (&optional arg)            ;; C-S-d
sp-end-of-sexp (&optional arg)                  ;; C-S-a
sp-beginning-of-next-sexp (&optional arg)       ;; none
sp-beginning-of-previous-sexp (&optional arg)   ;; none
sp-end-of-next-sexp (&optional arg)             ;; none
sp-end-of-previous-sexp (&optional arg)         ;; none

Note that it maps many to commands to the Emacs default equivalent. When it's installed, just browse it's functions (they're all prefixed with sp-) to get a good feeling for it's scale.

There's a lot more to it, I'd recommend you have a look at the wiki

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