Understanding the obvious about the business is a given - as covered above already. Understand the business culture and in doing so identify the people that shape this culture. Also identify the people who are the actual decision makers and drivers of the business. Understand them as people as well as their approach to the business.
Spend time chatting to the developers in different environtments, one-on-one, down the pub, over lunch, as a department, as teams. And gain an understanding of them as people, their skills, talent, and experience - although this will all become very clear very quickly through their work. Also gain their tech view on the business. Earn their respect.
Get an undetstanding of the technology you will be responsible for. Dig into code, look at how apps are deployed etc. and find out the reasons/thinking behind the way/approach that has been taken.
I would do all of this in parallel as much as possible.