The inscribed stone, also known as the Mesha Stele dates from around 840 BC and tells of the greatness of King Mesha of Moab (in modern-day Jordan); it features points between words and vertical strokes to mark the end of sections that might be comparable to biblical verses.
Most historians believe that punctuation as we know it today was invented to show how a text should be read aloud. By the fifth century BC, Greek playwrights were using some basic symbols to show where actors should pause, and the scholar Aristophanes of Byzantium (c257– c185 BC) invented a formal system of punctuation. He also designed accents to aid pronunciation.
Most other ancient written languages in their original forms – Sanskrit, Arabic, Korean, Chinese, Japanese, etc – used little or no punctuation, though some Chinese scrolls from around 400–300 BC sometimes used symbols to denote chapter and sentence endings.
Punctuation in its modern form owes a lot to the Renaissance and, particularly, the Italian scholar and printer Aldus Manutius (1449–1515), but also to the Reformation and the printing of Bibles in local languages. These were, of course, intended to be read aloud. Our modern system of punctuation didn’t emerge till the 19th century.
English/American punctuation is now used more or less wholesale across Europe; aspects of it have been adapted in most other parts of the world.