They're proper almost any time that week is the fundamental unit of aggregation. I've commonly used these for naming folders (or more recently AWS S3 buckets) for storing log files or periodic data dumps. For example a structure like
/year/week/date.log
If you don't want uneven sized weeks you want to use the ISO year and week. Here's an example with date, we're already in the first week of 2015:
% date '+ %G/%V/%F.log'
2015/01/2014-12-29.log
and 3 days from now still will be:
% date -v+3d '+ %G/%V/%F.log'
2015/01/2015-01-01.log
Contrast that with the "non-ISO" year and week:
% date '+ %Y/%W/%F.log'
2014/52/2014-12-29.log
in three days that rolls over to a new week
% date -v+3d '+ %Y/%W/%F.log'
2015/00/2015-01-01.log
And we'd have 2 folders or buckets containing a less-than-usual number of log files.
The OpenBSD manual under strftime (referenced in the date man page) shows "%G is replaced by the ISO 8601 year with century as a decimal number." Which leads to http://en.wikipedia.org/wiki/ISO_8601 and http://en.wikipedia.org/wiki/ISO_week_date which says "The ISO 8601 definition for week 01 is the week with the year's first Thursday in it."
Our example is a couple of activity reports we send to the government where we need to have full weeks and they want calendar years and not budget years[1]. I seem to remember payroll for some uses the same scheme (yep, we pay weekly). Plus some internal reporting the the ISO date makes nice since we have a 2 week break which includes Xmas and New Years.
1) These are a bit of odd ducks actually. Most government reporting we do is based on Federal Fiscal years which start Oct 1. I remember in the 90's one foxbase function that did a similar algorithm except centered on Oct 1 and defined the first day of the week as Sunday.
Say you're doing weekly data processing that always needs to be Sun - Sat. You'd want yesterday to be the start of week 1 for 2015. Or any sort of data slicing and dicing that allows viewing by week, you'd want everything from Sun - Weds of this week to roll up to week 1 of 2015.
(According to man on Mac OSX for G - "This year is the one that contains the greater part of the week (Monday as the first day of the week)"