This quote is often shortened/paraphrased to a condensed version: "Those who would trade liberty for safety deserve neither."
In an American context, Franklin's line plays on the idea that liberty is the thing we would be protecting by choosing safety. In opting to give up liberty in favor of safety, we are essentially gaining nothing.
The thing we value most (liberty) is lost if we elevate safety to a place of primary value. The essence of this idea, to me, is that liberty entails some necessary degree of uncertainty. Liberty stands in opposition to tyranny, to paranoia and to knee-jerk militarism.
When people have liberty (freedom of choice, freedom of speech, freedom of action, freedom of movement, etc.), they are not being controlled and so might go "out of control" and use that liberty to harm others. If a position was adopted that sought to curb liberty so that people would or could not go "out of control" then people would effectively be controlled. In opting for safety of this kind, freedom of movement, freedom of choice, freedom of speech and freedom of action would be reduced or eliminated.
Thus, in choosing safety over liberty one is choosing safety instead of liberty.
What Benjamin Franklin is trying to say in this quote is that personal liberty is the most important thing in a democratic society.
In democratic societies, we typically say that there is a tradeoff between liberty and safety. We see this tradeoff most clearly in the areas of policing and of anti-terrorism. A recent example of this is the revelation that the government has been collecting data on who we call on our phones. We say that we have to be willing to give up some of our freedoms so that the government can protect us from criminals and terrorists.
Franklin is rejecting this idea. He is saying that no one ought to be willing to give up any “essential liberty.” When he says this, he is claiming that liberty is the most important thing. He is saying that giving up liberty in order to get safety is something that is really bad. It is so bad that we do not deserve to have either liberty or safety if we are willing to give liberty up. This means that liberty is the most important thing.
The above answers are historically inaccurate and fundamentally wrong, although they do reflect the common misunderstanding of his original statement.
Some historical context is needed. It is the French & Indian war, and the Pennsylvania Legislature is trying to tax the Penn family in order to raise money to help the folks on the frontier defend that area. The Governor keeps vetoing all the bills, mostly because he was an appointed minion of the Penn family. The Penns have offered a financial donation in exchange for the Pennsylvania legislature conceding the right to tax the Penn's.
The original quote is found in a letter to the Governor of Pennsylvania, and the letter is commenting unfavorably on those persons in the frontier areas (and the Pennsylvania legislature) who are willing to exchange the right to tax the rich in exchange for a payoff to buy a little temporary security by means of a bribe to buy weapons with.
Most modern interpretations of this famous quote assume that Benjamin Franklin was referring to sacrificing personal liberty in exchange for government provided security, although that was not his intention at all. He was actually supporting a stronger government more capable of enacting legislation to protect it's populace.