There are a number of definitions of Business Analysis.

For example, the IIBA provides the following:

Business Analysis is the practice of enabling change in an organizational context, by defining needs and recommending solutions that deliver value to stakeholders. The set of tasks and techniques that are used to perform business analysis are defined in A Guide to the Business Analysis Body of Knowledge® (BABOK®Guide). IIBA Definition

This partially covers what I have experienced. In large organizations, there is a significant division of labour within systems departments. This division of labour allows for a greater specialisation of roles. There are project managers, business analysts, developers, and testers. In smaller organizations, the business analyst can fulfill all of the roles. Most commonly they do the business analysis and the testing.

Based on my experience, I have arrived at the following definition of Business Analysis:

Busines Analysis is the process through which issues or problems are examined in sufficient detail to enable the identification of one or more possible solutions, guidance is provided to enable the selection of the correct solution, and verification is undertaken to confirm that the solution is working as expected.