Q:

Is HTTPS secure?

I'm developing a iPhone App that connects to a https:// link to authenticate the user.
From what I understood all traffic that goes to a server that has a private key on 256 bits is secured and cannot be caught so there is no need to encrypt the data again and it can be sent as plain text along the HTTPS connection.
After reading this blogpost:
http://wirewatcher.wordpress.com/2010/07/20/decrypting-ssl-traffic-with-wireshark-and-ways-to-prevent-it/
I don't understand how that traffic can be caught with Wireshark if it's secure. 
Edit:
I've re-read the article and from what I understand you have to have access to the server's private key to do this.
What I don't understand is how this guy did it here because I don't think he had access to that.
http://techcrunch.com/2013/11/25/quizup-privacy-violations/
http://kylerichter.com/our-responsibility-as-developers/

A:

If you read carefully: 

[...] the output of this command is two files, testkey.pem (containing a
  1024 bit RSA private key) and testcert.pem (containing a self signed
  certificate)

And further down:

Once SSL is selected, there’s an option on the right to enter an “RSA
  keys list”. Enter something like this:
10.16.8.5,443,http,c:\openssl-win32\bin\testkey.pem
You’ll need to edit the server IP address and path to testkey.pem as
  appropriate.

And more:

Protection of one’s private key is at the core of any system using
  asymmetric keys. If your private key is compromised, the attacker can
  either masquerade as you or they can attempt to carry out decryption
  as outlined above.

Basically in the tutorial, the author is giving wireshark the private key to decrypt the trafic - intentionally. That private key MUST be kept secret on the server and shouldn't be accessible by anyone in a real life scenario. He gives some tips on enhancing security like using the Diffie-Hellman method of exchanging keys.
Bottom line: YES, it's secure.
Here are some nice videos that explain public key cryptography:
http://www.youtube.com/playlist?list=PLB4D701646DAF0817

