They are typically people who know a lot about the domain of business but also have some technical background. This doesn't necessarily involve statistical data analysis, but they have to analyze business, as the title suggests - which typically involves business data. They usually work closely with technical people (like programmers) and help them to understand the business goals, sometimes through data, sometimes through their knowledge of domain.
It's about analyzing data to help decision makers make less risky decisions, they typically also need to know the domain to analyze - finances, insurance, medical stuff, etc. Here they should be able to do some statistical analysis, e.g. being able to spot extreme values, suspicious activities, fraud, etc.
It can be simply a risk manager in insurance. But it may involve other things, not related to Data Analysis per se.
(Sometimes referred as Information Analyst) The title is clear. This person must be able to analyze data typically with statistical and data mining tools
Sometimes it's a data analyst who works for marketing
Business Intelligence Developer/Analyst
These people develop and manage data warehouses, but they also build reports for the business and build predictive models. Business Intelligence is a very broad area (see wiki) which includes OLAP analysis, data analysis and data mining
Data Warehouse Developer
(Sometimes ETL Developer). These people know how to collect data from different sources and put in to the common storage (data warehouse) so it can be analyzed. Typically it's a part of Business Intelligence, so they are also involved into building some reports, doing OLAP and data mining.
This is just a fancier name for a Data Warehouse Developer. It has to do with the same things, including building some statistical models (occasionally)
The list is far from comprehensive, so feel free to suggest other things