"Nothing rests; everything moves; everything vibrates" -The Kybalion
Vibration can be understood as the way energy moves within a particular entity. As everything is made of energy, and everything has a vibration, the way something or someone vibrates is what determines the experiences that are attracted. This is closely related to the Law of Attraction, which tells us that we attract those things that are in harmony with our present rate of vibration.
The crucial word in the last paragraph is "present," for your rate of vibration -the kind of energy you send out to the universe- can and does change all the time. It may not seem this way; in fact, it may seem that little in yourself or the world changes much. This is because there is a tendency for inertia to set in -for a certain pattern of vibration to repeat itself over time. Still, we can observe that everything actually does change. Seasons pass, living things are born, grow and eventually die; the economy and the weather also change, though certain cycles are repeated.
There is one major difference between human beings and the other types of examples just mentioned -we have free will, which means we have the ability to change our vibration based on our intent. Our vibration is determined by our thoughts, beliefs and emotions. Our emotions are actually the "barometer" of our vibration -they tell us the results of the vibration we are putting forth at any given moment.
Our emotions can also tend to perpetuate the thoughts and beliefs we've held in the past, which can sometimes be a trap. If we want to change something in our life, we have to break the usual pattern of thoughts and emotions. To do this we may have to do something to break the pattern; a diversion of some kind. It's important, when we are feeling negative emotions, to realize that this is telling us something important about our vibration and what we are presently attracting. If we can divert ourselves from this negativity, even for a short time, we can at least return to a more neutral state and then focus on creating more positive beliefs that will lead to more desired emotions and then outcomes.
What we must remember about vibration is that we are always vibrating some kind of energy, which is attracting something in the "external" world. This is unavoidable. The only choice we have is how we want to vibrate -what patterns of energy we want to manifest- which will determine our experiences. The universe is made of energy in constant vibration, energy is never static. Everything is always changing, so we don't have the choice of freezing everything in place as it is, or appears to be now. We do, however, have the choice of "going with the flow," and being in harmony with the changes. This does not mean simply being resigned to accepting the world the way it is. When we are truly in harmony with the flow of energy, we are part of the it, so we are part of that which chooses how things will work out.
There are various practices that can help us vibrate in a more positive or harmonious manner -affirmations, meditation, physical exercise (especially anything that has us breathing deeply) and fostering healthy relationships. The main thing, however, is to recognize that we are beings made of energy in motion, and that we can choose our rate of vibration based on the thoughts and mental pictures we are broadcasting at all times. This means we must take responsibility for the circumstances around us, as they are nothing more or less than our own creations.