How does the college course 101 numbering system work?
A common system works roughly as Najib Idrissi describes: courses numbered 100-199 are first-year courses, which either have no prerequisites or only high school-level prerequisites.  Courses numbered 200-299 are second-year courses, which have 100-level prerequisites, and so on.

But this system is by no means universal in the US, nor does the rough description above capture all aspects of it accurately.  The "and so on" 
 above would lead you to guess that 400-499 are the most advanced undergraduate courses, and 500+ are graduate courses.  And that's the case at some universities.  But at my current institution, 300-399 designate the most advanced courses intended primarily for undergraduates (including those in their fourth year), and courses starting at 400 are graduate classes.  At another institution I've been at, "lower-level" undergraduate courses are 1-99, "upper-level" graduate courses are 100-199, "lower-level" graduate courses are 200-299, and "upper-level" graduate courses are 300-399.  And in any of those systems, you can't always guess from the number alone the relationship between Basket Weaving 125 and Basket Weaving 147.

To address your question about the online chemistry course, you can't even assume that Chemistry 101-106 even exist at the institution in question; if they do, they may or may not have any clear relation with 107.  When I was an undergraduate, there were two distinct introductory chemistry sequences for different audiences: 105-106 and 107-108.  So there was no 101, and 106 was a more advanced course than 107.

So if you want to know the place of a specific course in the curriculum, you have to consult the course offerings of the specific institution.

tl;dr (summarizing this and other answers, and many more details in comments): There is no one system for course numbers, even at a given institution.  At best you can make a rough guess about a course number's meaning.  If you really want to know, you need to find information from the specific department.