Why was it important for that date format to be standardized by the International Organization for Standardization (ISO) ?

Because many different countries use different formats for the date.

The most important difference is the order of the year, month and day.

When writing a date with numbers, some countries stick to a sequence order more natural to their language. In the USA for example, they usually write dates in the format MONTH-DAY-YEAR.

Other countries use DAY-MONTH-YEAR, like many countries speaking French, because it matches the sequence in the written language.

Others use YEAR-MONTH-DAY, which makes sense and facilitates a lot the sorting.

If you want to represent for example January 10 only in numbers, because both month and day numbers are below 13 ... someone could easily mistake that as October 1st, if he doesn't know the exact sequence you're using.

Problem becomes bigger if you write the year with only 2 digits ... since we are now in year 19 ... that could also be mistaken with a day. If I show you for example 09-02-10, which date am I talking about?

There's also another minor difference in terms of separator, like the dash (-), the period (.), the apostrophe (') and a few other symbols are used to separate the date elements.