A Business Analyst is someone who works with business users in companies, mainly helping them with their information needs. The position is an IT position by and large, although more and more the business analyst may be part of the business unit for which they work. So, if the business wants to change the sales process or the forecasting process, or they want to install a big system such as SAP etc., the business analyst will work with users and customers to define their needs, help to specify and communicate this need to the IT service, and during the implementation of the system they will work on training the users, defining the overall measurements and reports for the system, and helping with the testing of the system before it goes live. Large companies are continuously changing nowadays, so business analysts are quite busy!
The term is relatively generic, so you will also see people who are referred to as business analysts involved in large-scale data analysis, identifying trends and opportunities in the market. The same would be true for financial analyses of companies.
I am a business analyst