A development environment is a combination of a text editor and the Python interpreter. The text editor allows you to write the code. The interpreter provides a way to execute the code you've written. A text editor can be as simple as Notepad on Windows or more complicated as a complete integrated development environment (IDE) such as PyCharm which runs on any major operating system.
Python code needs to be written, executed and tested to build applications. The text editor provides a way to write the code. The interpreter allows it to be executed. Testing to see if the code does what you want can either be done manually or by unit and functional tests.
Here's what I (the author of Full Stack Python, Matt Makai) use to develop most of my Python applications. I have a Macbook Pro with Mac OS X as its base operating system. Ubuntu 14.04 LTS is virtualized on top with Parallels. My code is written in vim and executed with the Python 2.7.x interpreter via the command line. I use virtualenv to create separate Python interpreters with their own isolated application dependencies and virtualenvwrapper to quickly switch between the interpreters created by virtualenv.
That's a common set up but you can certainly write great code with a much less expensive set up or a cloud-based development environment.
vim is my editor of choice and installed by default on most *nix systems.
emacs is another editor often used on *nix.
Sublime Text versions 2 and 3 (currently in beta) are popular text editors that can be extended with code completion, linting, syntax highlighting and other features using plugins.
PyCharm is a Python-specific IDE built on JetBrains' platform. There are free editions for students and open source projects.
Wing IDE is a paid development environment with integrated debugging and code completion.
In the past couple of years several cloud-based development environments have popped up. These can work great for when you're learning or stuck on a machine with only a browser but no way to install your own software. Most of these have free tiers for getting started and paid tiers as you scale up your application.
If you're considering the cloud-based development environment route, check out this great article comparing Cloud9, Koding and Nitrous.io by Lauren Orsini. She also explains more about what a cloud IDE is and is not.
Real Python has an awesome, detailed post on setting up your Sublime Text 3 environment as a full-fledged IDE.
The Hitchhiker's Guide to Python has a page dedicated to development environments.
Choosing the best Python IDE is a review of six IDEs. PyCharm, Wing IDE and PyDev stand out above the other three in this review.
