Here's the definition of Business Analysis taken from the current version (Version 3) of the BABOK® Guide:
"Business analysis is the practice of enabling change in an enterprise by defining needs and recommending solutions that deliver value to stakeholders. Business analysis enables an enterprise to articulate needs and the rationale for change, and to design and describe solutions that can deliver value.
Business analysis is performed on a variety of initiatives within an enterprise. Initiatives may be strategic, tactical, or operational. Business analysis may be performed within the boundaries of a project or throughout enterprise evolution and continuous improvement. It can be used to understand the current state, to define the future state, and to determine the activities required to move from the current to the future state."
Here's the definition from the previous version (Version 2.0) of the BABOK® Guide:
"Business analysis is the set of tasks and techniques used to work as a liaison among stakeholders in order to understand the structure, policies, and operations of an organization, and to recommend solutions that enable the organization to achieve its goals.
Business analysis involves understanding how organizations function to accomplish their purposes, and defining the capabilities an organization requires to provide products and services to external stakeholders. It includes the definition of organizational goals, how those goals connect to specific objectives, determining the courses of action that an organization has to undertake to achieve those goals and objectives, and defining how the various organizational units and stakeholders within and outside of that organization interact.
Business analysis may be performed to understand the current state of an organization or to serve as a basis for the later identification of business needs. In most cases, however, business analysis is performed to define and validate solutions that meet business needs, goals, or objectives.
Business analysts must analyze and synthesize information provided by a large number of people who interact with the business, such as customers, staff, IT professionals, and executives. The business analyst is responsible for eliciting the actual needs of stakeholders, not simply their expressed desires. In many cases, the business analyst will also work to facilitate communication between organizational units. In particular, business analysts often play a central role in aligning the needs of business units with the capabilities delivered by information technology, and may serve as a "translator" between those groups.
A business analyst is any person who performs business analysis activities, no matter what their job title or organizational role may be. Business analysis practitioners include not only people with the job title of business analyst, but may also include business systems analysts, systems analysts, requirements engineers, process analysts, product managers, product owners, enterprise analysts, business architects, management consultants, or any other person who performs the tasks described in the BABOK® Guide, including those who also perform related disciplines such as project management, software development, quality assurance, and interaction design."