Systems Analysis is, as the name states, the analysis of systems!
The systems that we are talking about are the systems within organisations and businesses - systems of communication, financial systems, manufacturing systems, etc. - basically the systems that make the organisation or business work.
A person who analyses systems is known as a Systems Analyst.
Often systems analysts are employed by organisations of businesses to help them improve their systems and so become more efficient, and for businesses, more profitable.
A systems analyst would generally perform the following steps in the order shown...
Research
Collecting information about the present system works
Analysis
Examining out how the present system works and identifying problems with it
Design
Coming up with a new system that will fix the present systems problems
Production
Creating the new system from the design
Testing
Checking if the newly created system works as expected
Documentation
Creating documents that describe how to use the new systems, and how it works
Implementation
Replacing the present system with the new system
Evaluation
Checking that the new system meets all expectations