The purpose will answer the question, "What problem will the program solve?" It could be stated like

I need to be able to scramble the letters of my name.

or

Big Computer Corp. needs to track the sale and inventory of its products.

From these simple definitions, you can get more complex.

Big Computer Corp. needs to track the sale and inventory of its products.

Track sales figures, including quantity sold at price, quantity sold after advertising, ...

Track inventory and indicate when an item is low. ...

It's often a fine line between a purpose statement and a task statement. Often, your purpose statements will translate directly into a task statement:

Purpose: Track inventory
Function: Track inventory