As a consultant, I worked in various domains such as utility, telecom, aeronautics, finances, insurance, etc and I've faced the problem of not knowing very much about the domain I was entering. With time, I discovered a very simple method that works: being actively curious.
- Request a one to one introductory meeting with your supervisor with the purpose of getting them to explain the business domain (the big picture). It should not last more than 4 hours (or you will get bored and your supervisor exhausted). Prepare your questions in advance. Take notes.
- Ask the supervisor for a field visit. When I worked in the telecom industry, I asked to visit the router and transmission rooms as well as the NOC (Network Operations Center). It helped the team building the software to understand the purpose instead of blindly writing code. We knew why our stuff was useful and more importantly, who will be using it, and how.
- Have frequent lunches with suits. More frequently, I would say, than with fellow programmers. They love to talk about their stuff and if you listen carefully, you will learn lots of amazing things. Be prepared to share some amazing stuff with them too or they will soon find you very boring.
- When you have the chance, visit the departments. Ex: when I had to work with a marketing manager of a big finance institution, I asked how our applications helped them and what was her routine. By actively listening to her, I was able to find out new stuff to automate and make her work life easier. I suggest you make a physical visit rather than a phone call. This means you can see her doing the thing and more importantly, using your application! What is obvious for you may not be so obvious to the rest of the world.
- Buy books on the domain and watch youtube videos. Read your domain's information websites as well. Give priority to higher level literature. Books that are too technical could be boring or impossible to understand in the beginning. What you need is general concepts to fuel conversations and learn more.
- Talk about it to your friends & family often. Talking about your stuff will help you integrate the huge amount of information you must learn. Prepare an elevator pitch and be prepared to give details. Don't hesitate to write it down so it is easy to remember.
- Read all the news your company publishes. Including annual reports. In fact, the first thing to do when you are hired by a new company, is consult their website and publications.
- When you don't understand something, don't hesitate to ask the guy in the company (email preferred) that can answer your question. The worse thing that could happen is being told that (s)he has no time for that.
Remember this: the developer that knows the domain very well is no longer just a simple developer. You are a little more than that. And so is your market value.