I need help understanding the use of | in a specific context. I am reading the wikipedia article on Multiple Sequence Alignments and came across some notation I haven't seen yet, specifically $x_i|i = 1,...,r$ in the statement $L > max \{x_i|i = 1,...,r \}$. I was wondering if anyone can shed light onto what that means. Thanks for any help.

Given the context of your question, it would mean 'such that'; 'so that'; 'everywhere'. 
Or in other words: 'L is greater than the maximum of the set $x_1, x_2, ...x_r$'
In other contexts, it can mean various other things. I suggest you take a good look at:
https://en.wikipedia.org/wiki/List_of_mathematical_symbols
