In German a date is written like this:
10. Januar 2014
There is of course a space between all "words". The dot behind the number for the day is a writing convention for ordinal numbers. E.g.
10 is "ten" and
10. is "tenth" in German orthography. So the above example reads "tenth january two thousand fourteen", if you translate it.
Of course the month can be abbreviated as a number, too. Using the same example from above, we would get:
10. 1. 2014 or 10. 01. 2014
Note the spaces behind the dots, as what you write is considered a word, which is only represented as a number. This, with spaces, is how most people write a date. (Typographers recommend an eighth of a quad instead of a full space.)
But there is in fact an industrial norm (DIN 5008), which defines design rules for text (such as business letters), and this norm requires that you writes dates without a space:
10.1.2014 or 10.01.2014
Looking through some of my recent letters I can confirm that government institutions and my university use the format without spaces. (The expanded version, with the month spelled out, always must have spaces.)
In handwriting or informal letters (written by non-secretaries), the space behind the dot is the norm.
Basically the German convention to write dates rises naturally from how dates are spoken.
The dot is a common convention for ordinal numbers, and in German the day is said before the month, so, if you think about it, it is not actually a convention for writing dates at all, but how a German would naturally write a date if there was no convention.
This natural way to write dates as it was habitually found in letters at the time was defined as an orthographic convention in 1928 through the "Guidelines for the Treatment of Business Mail" by the German government.
I don't know where the dot to mark an ordinal number in numeral form came from.