"To network" simply means to meet and interact with other people. It is a good way to make business contacts or to find work when you're looking for a job. For example, if you work at a service job and one of your regular customers (with whom you've developed a friendly relationship) owns a car dealership, you might be able to get a good deal on a new car when you're shopping around.
There is an old proverb that says "variety is the spice of life," so when this gentleman refers to "pulling from the spice cabinet," he simply means he's adding some variety to his daily life. Most likely his second, part-time job is something completely different than what he does full-time, so that keeps him from getting bored.