FUNCTION

The period is the punctuation symbol that marks the end of a sentence.
It is also used to replace sections of letters in abbreviations or in numbers to indicate thousands (in European languages, while a comma is more popular in English).

In the digital world, the period is often used to separate information from individual categories (domain-name.com).

HISTORY

In Ancient Rome, the period (which looked like a dot placed at middle height) was used to separate words. Scribes of medieval Europe started using it to separate sentences (words were separated by a space), and shifted it to the baseline, which has been kept as is ever since.

DESIGN

In most scripts, the period is a dot placed on the baseline. In Latin script, it is about the same size as the dot on the letter i.
In many other languages and scripts, sentences end with different symbols. For example, in Chinese and Japanese, the period is a hollow circle, placed at the base or centered in relation to the characters.

TYPOGRAPHIC RULES

When used to end a sentence, it has no space before, and it is followed by a space for the eventual next sentence.
It has no space before the next letter in an abbreviation. In American English, when used in a quote, it is preferred to place the, quotes before the period. While in British English the period goes after the quotes.

In numbers with decimals, it is used as such:
(European languages) 15.000,05
(English) 15,000.25