Python's built-in ("batteries included") string formatting capability is especially useful in ArcGIS Python (arcpy) scripting, where you often have to build complex SQL or calculate expressions.
For example, this SQL expression could easily be mangled:
(Note that in Python, double quotes in single quotes [and vice versa] are recognized as literals.)
using .format() is much easier to write, read, and debug:
The Calculate Field tool requires embedded quotes for its Python sub-process to recognize literal strings.
The complexity is much easier to handle using .format().
Some formatting would be very painful without using Python's formatting functionality:
Useful examples, and references: Python String Format Cookbook