What are the differences between -std=c++11 and -std=gnu++11?

As you have found out yourself, the difference between the two options is whether GNU extensions that violates/extend the C++ standard are enabled or not. The GNU C++ extensions are described here. You can also use most of the GNU C extensions (described here) in your C++ programs. It would be also useful to read about the -Wpedantic GCC option here.

Note that some extensions can still be in effect when using -std=c++11, as long as they do not contradict the standard. For instance, when using the MinGW compiler, I need the extensions for a working Boost.Lexical_Cast. But, as long as you don't use any of them, you are better off sticking to the standard without extensions for maximum portability. This might come in handy if you find yourself forced to change compiler.