Providing an answer is turning into a week-long project. Luckily I started it on Friday, and not on Sunday or Monday!
In our normal calendar, weeks (a set of 7 days) fall across the boundaries of the months and years. Here's how we would normally display them in the USA, if we start the week with Monday, or Sunday [click the graphic if you want a larger version]:
One advantage to numbering the weeks is that you can choose certain dates in advance - for example, the company annual report deadline can be Monday of week 15 in every year. Or paychecks will be issued on Fridays of evenly-numbered weeks.
All companies in your country can use the same systems - for example, a food producer's system can say a packaged meal was prepared in 2011 during Week 25 on Day 3 (the actual ISO 8601 code is 2011W253) plus "use within 15 weeks" and a retailer's system could easily calculate the date that food will be stale.
Are there disadvantages? Here are some potential issues:
- This system has leap weeks - some years have 52 weeks and some have 53 weeks
- Some days in a year may be assigned to weeks from the previous or future year
- There are no set relationships between weeks and months
So far (just in case you were worried) we do not teach the ISO 8601 system to elementary school kids. But as an adult, you wanted to know this, right?