CentOS 6 must have 2.6.6 as main install because of some system applications that depend on it.
Newer versions of Python are available in /share/apps/python/.
To use these version, add the desired version's path to your search path, or call the binaries directly.
Or you can use the Software Collections scl tool.
Run scl -l for a list of installed collections. Then, e.g., to use Python 2.7, run this:
scl enable python27 bash
This will start a new shell that's set to use python 2.7 (run which python and python –version to verify).