An Android/Iphone app will be accessing application data from the server. [Django-Python]
How can I secure the communication with the mobile app ?
Expec
You're working on bad information. SSL can absolutely authenticate the client, it's just not something that is done for the bulk of SSL as the protocol is (or, atleast was) typically used to protect e-commerce sites where authentication of the server was important but doing so with the client was not important and/or not feasible. What you want to do is employ mutually-authenticated SSL, so that your server will only accept incoming connections from your app and your app will only communicate with your server.
Here's the high-level approach. Create a self-signed server SSL certificate and deploy on your web server. If you're using Android, you can use the keytool included with the Android SDK for this purpose; if you're using another app platform like iOS, similar tools exist for them as well. Then create a self-signed client and deploy that within your application in a custom keystore included in your application as a resource (keytool will generate this as well). Configure the server to require client-side SSL authentication and to only accept the client certificate you generated. Configure the client to use that client-side certificate to identify itself and only accept the one server-side certificate you installed on your server for that part of it.
If someone/something other than your app attempts to connect to your server, the SSL connection will not be created, as the server will reject incoming SSL connections that do not present the client certificate that you have included in your app.
A step-by-step for this is a much longer answer than is warranted here. I would suggest doing this in stages as there are resources on the web about how to deal with self-signed SSL certificate in both Android and iOS, both server and client side. There is also a complete walk-through in my book, Application Security for the Android Platform, published by O'Reilly.