Note: See updates about WhatsApp man-in-the-middle exploit, potential WhatsApp backdoor which can allow snooping, and article on how the CIA can bypass WhatsApp message encryption by accessing the phones directly below:
How to block:
Generally, this means your country will either block the website/applications IP address Range which will prevent packets from reaching the website or null route the BGP/AS number (blocking these IP's from being routed).
Getting around a blocked IP restriction:
There are MANY ways to do this but generally this means you will want to use a VPN provider in another country or a tool like Tor if either of those are an option.
Note: There are many Tor-based web browsers for various phones. These would be a good solution for access to web pages for your phone but this won't secure connections from your phones other apps.
There are many VPN solutions which will work well on mobile devices. In many cases this may be easier to configure if it's not outlawed.
If neither of those are an option (legally or technically) you may want to check and see if the application or website are accessible via IPv6. If there is an IP restriction it may only be blocked on the IPv4 addresses and not the IPv6 addresses so you may be able to connect directly without using any type of encryption or service which is currently outlawed in your country.
Note: It is very important to understand your local laws when doing any of this and likely worth consulting an attorney to make sure you are not unknowingly breaking any laws in the process.
Update: This post by Bruce Schneier about a man-in-the-middle exploit for WhatsApp is very relevant to your question.
Update2: This post discussing a potential backdoor discovered in WhatsApp which allows snooping of encrypted messages.
For additional technical clarity, this post is also useful to read
Update3: The most recent Wikileaks release of CIA documents shows how the CIA can access the phone to read WhatsApp messages effectively bypassing its encryption. It's likely other governments can do the same thing using the same or similar methods.