FUT is the short form for Functional Unit Testing. This is usually performed in an SAP system where functionality of each unit is tested to ensure that the overall functionality of the software or application should work as per defined benchmarks.
You may even call it a function under test kind of testing. However, the goal of the process is all about meeting the functionality related objectives. But it is an approach that helps you to take the product to the market faster and therefore may need you to make frequent iterations on test cases.