Mantid ships with many predefined Algorithms.
Python algorithms provide a mechanism to define extra algorithms at run time that Mantid treats exactly the same as if they were shipped with the package.
Benefits of an algorithm over just writing in a script:
Create workspaces that are seen by Mantid - Improved performance for your specific task
History tracking - Python processing in a standard script isn’t tracked in the workspace history but it is through a Python algorithm
Free GUI - All algorithms have a default auto-generated input GUI