From the excellent Mindfulness in Plain English:
Concentration and mindfulness are distinctly different functions. They each have their role to play in meditation, and the relationship between them is definite and delicate. Concentration is often called one-pointedness of mind. It consists of forcing the mind to remain on one static point. Please note the word force. Concentration is pretty much a forced type of activity. It can be developed by force, by sheer unremitting willpower. And once developed, it retains some of that forced flavor. Mindfulness, on the other hand, is a delicate function leading to refined sensibilities. These two are partners in the job of meditation. Mindfulness is the sensitive one. It notices things. Concentration provides the power. It keeps the attention pinned down to one item. Ideally, mindfulness is in this relationship. Mindfulness picks the objects of attention, and notices when the attention has gone astray. Concentration does the actual work of holding the attention steady on that chosen object. If either of these partners is weak, your meditation goes astray.
Concentration could be defined as that faculty of the mind that focuses single-pointedly on one object without interruption. It must be emphasized that true concentration is a wholesome one-pointedness of mind. That is, the state is free from greed, hatred, and delusion. Unwholesome one-pointedness is also possible, but it will not lead to liberation. You can be very single-minded in a state of lust. But that gets you nowhere. Uninterrupted focus on something that you hate does not help you at all. In fact, such unwholesome concentration is fairly short-lived even when it is achieved— especially when it is used to harm others. True concentration itself is free from such contaminants. It is a state in which the mind is gathered together and thus gains power and intensity. We might use the analogy of a lens. Parallel waves of sunlight falling on a piece of paper will do no more than warm the surface. But if that same amount of light, when focused through a lens, falls on a single point, the paper bursts into flames. Concentration is the lens. It produces the burning intensity necessary to see into the deeper reaches of the mind. Mindfulness selects the object that the lens will focus on and looks through the lens to see what is there.
Concentration should be regarded as a tool. Like any tool, it can be used for good or for ill. A sharp knife can be used to create a beautiful carving or to harm someone. It is all up to the one who uses the knife. Concentration is similar. Properly used, it can assist you toward liberation. But it can also be used in the service of the ego. It can operate in the framework of achievement and competition. You can use concentration to dominate others. You can use it to be selfish. The real problem is that concentration alone will not give you a perspective on yourself. It won’t throw light on the basic problems of selfishness and the nature of suffering. It can be used to dig down into deep psychological states. But even then, the forces of egotism won’t be understood. Only mindfulness can do that. If mindfulness is not there to look into the lens and see what has been uncovered, then it is all for nothing. Only mindfulness understands. Only mindfulness brings wisdom.