I think the premise should be rephrased as "The more SKILLS you get, the more chances you get to be employed". However, what the original phrase means is that the more you know the farther you go. It is very simple: When you have the information, you have the power. When you have the means, you have the way. The basic gist of this idea is basically that when you are able to expand your intellectual horizons you will see things differently, and you will feel prepared to undertake just about any challenge. You will be confident, sure of your self, and safe in your own abilities. That is the reason why education is so important: It is a conduit to many possibilities. It is a key to the future, and to a better life. Nobody has ever succeeded by being an ignorant, unless they have inherited their money. That is basically what it means.
The meaning behind this quote is that education helps a person be able to make more money later on in life. The quote is based on the idea that the best jobs are the ones that require a good deal of education.
If you, for example, do not have a high school education in the US, the jobs that are open to you are quite limited. You are most likely going to have to start off in some job that is relatively unskilled (like working in a food packing plant) and does not pay very well. By contrast, if you go to college or beyond, you can be a store manager or a teacher or a lawyer or a doctor. These jobs require more education, but they also pay better and are less likely to be cut in bad times.
So, the meaning of this quote is that the jobs that pay the best and are the most stable are typically ones that require an education.