What does the symbol |_ mean?

In Cajori's "A History of Mathematical Notations", this symbol is attributed to Thomas Jarrett and means $n!$. See article 447 of Cajori's book for the attribution and articles 448 and 449 for the history of its use, mainly in the 19th century.

This is the notation once used for factorials. I have a copy of Hall and Knight's Higher Algebra (1964 reprint, first published in 1887) that uses this notation. See http://www.math.uconn.edu/~kconrad/math1132s14/handouts/hallandknight.pdf for a two-page scan from the book, which I show my students sometimes, where on the first page the notation is defined and n! is mentioned as another notation that is "sometimes used."

The Wikipedia page for factorials says the use of ! for factorial was introduced in the early 1800s.

From the context, it seems to mean factorial ($n!=1\cdot 2 \cdot 3 \cdot \ldots \cdot n$). But I've never seen it before.

Adding to @Bernard Masse, the history of notations for products of terms in arithmetical progression is quite long. The following is taken from Christian Kramp, 1808, Elémens d'arithmétique universelle (pdf), p. XI-XII:

where $1^{p|1}$ would denote the (nowadays) factorial.

He used the term "faculties (facultées en French)", acknowledged Louis Arbogast for the term "factorial (factorielles)", and on page 348, he introduces the notation $p!$ for $1^{p|1}$ (additional details in History of notation: "!"). You can find this from Article 445 (Volume 2, Page 66) in Florian Cajori, 1993, A History of Mathematical Notations (Dover Publications).

From Article 447, Cajori mentions Thomas Jarrett (1805–1882) for his extensive study of algebraic notations, An essay on algebraic development: containing the principal expansions in common algebra, in the differential and integral calculus, and in the calculus of finite differences, 1831, Page 15, Article 38, you find:

$$\begin{array}{|c}p\\\hline\end{array}=p(p-1)\ldots 1$$

The first example is a well known proof of Euclid's result about infiniteness of primes; one takes a prime number $p$, then does $$ N=1+p! $$ and shows that $N$ is not divisible by $p$ nor by any smaller prime, because each one divides $p!$. So there exists a bigger prime than $p$, because $N>1$ is divisible by a prime. This means $\begin{array}{|c}p\\\hline\end{array}=p!$ (sorry for the bad emulation of the symbol); it could mean the primorial, that is, the product of all prime numbers from $2$ up to $p$, but this interpretation would contradict the usage in the second example.