How to access list data in Sharepoint from an external application?

My apologies if this question is already asked but I did not find similar questions.

There is an intranet Sharepoint site which cannot be accessed externally. I have an external application which has nothing to do with Sharepoint. I want to access the data in the Sharepoint list and store it in my applications database. I want to poll the Sharepoint list so that the data is in sync. How can I go about doing this? I am new to Sharepoint development so I am looking for the correct route to take to do something like this.

The Sharepoint version is 2010 SP2. What about 2013 version? Would I need a different approach. I have managed to access data from Sharepoint-Online but the sharepoint intranet seem to be a whole different beast.