A rat line must be routed by a “trace”. A trace represents an actual copper path on a PCB. This means that two traces representing different nets cannot cross paths. This places a great deal of restrictions on how rat lines can be routed.
Fortunately, a multi-layer PCB allows you to connect a trace of one side (layer) of a PCB to another side (layer). While this flexibility does not seem significant, it does improve the availability of routing resources.
The mechanism to bring a trace from one layer to another is called a via. A via is, essentially, a plated through-hole that is not intended for a pin. Instead, its sole purpose is to connect a trace of one layer to another. Because a via is a plated through-hole, you should use only the drill sizes that are available to you (limited by the fabricator).