How does a FOR/NEXT loop work in AMPscript, and what is a common use case?

FOR @i = startValue TO endValue DO ... NEXT @i iterates a counter variable. The most common use is iterating over a LookupRows or LookupOrderedRows rowset:
%%[
SET @rows = LookupRows("Orders","Email",emailaddr)
SET @cnt = RowCount(@rows)
FOR @i = 1 TO @cnt DO
SET @row = Row(@rows, @i)
SET @product = Field(@row, "ProductName")
]%%
%%=@product=%%<br>
%%[ NEXT @i ]%%
Note that AMPscript does not support WHILE loops. All iteration must be done via FOR/NEXT with a known upper bound (use RowCount to get it).