What is the origin of the | (pipe symbol) in typesetting?
That is called the pipe.
Robert Bringhurst tells us:
Despite its importance to programmers and its presence on the standard ASCII keyboard, the pipe has no set function in typography. For drawing broken rules and boxes, a separate character from a specialized ruling font is commonly used. Also called a broken bar or parted rule.
One use of the pipe symbol in typesetting is for the (usually fifth) footnote at the bottom of a page. In this case, it is doubled and called parallels (||).
Talking of the asterisk and dagger, typographers Hoefler & Frere-Jones say:
Both characters have functions in genealogy and other life sciences, where the asterisk indicates the year of birth (*1499), and the dagger the year of death (†1561). There are standard fourth-, fifth- and sixth-order reference marks, too: they are the section mark (§), parallels (||), and number sign (#), after which the cycle repeats with doubles, triples, and so on: *, †, ‡, §, ||, #, , ††, ‡‡, §§, ||||, ###, *, †††, ‡‡‡, etc. Beyond three, numbered footnotes are always preferable, even if you are David Foster Wallace.
See some examples in my answer to this question.