Most people have very little control over their minds. Though they can certainly take control when they need to, in order to concentrate on a project or problem, for instance, when they are not concentrating, their minds wander, daydream, and chatter incessantly. They want things, even things that are very impractical to want, or very dangerous. They worry about things, even things that are very unreasonable to worry about. These desires and worries greatly influence people's moods, especially the negative ones that people become motivated to change.
The mind's desires and worries wouldn't matter so much - wouldn't have so much power over people's moods - if they didn't take them seriously. Most people do take them seriously, however. They are identified with their thoughts and feelings - embedded in them - lacking in a certain kind of perspective necessary to understand that just because something feels urgent doesn't actually make it urgent.
Without this perspective, people become defined by and overly identified with their moment to moment desires and worries and spend their time running around endlessly trying to satisfy them - a truly thankless and impossible task.
Meditation techniques are designed to help people grow a larger perspective on the contents of their mind. With this perspective, people can move from being their moment to moment worries and desires, to having their moment to moment worries and desires. Instead of being worried, people can start to understand that they are experiencing a worrying feeling. The same old worries and desires are still there after growing the new perspective, but now they are things you can manipulate and choose whether to take seriously or not, rather than things that define you as a person. Because the new perspective allows you to view your mental landscape in a new and powerfully freeing way, it is sometimes referred to as the "witness consciousness".
The term "meditation" refers to a family of methods; not to a single one. Any method that promotes the growth of the witness consciousness, the expanded perspective from which to view ones mind can be said to be meditation.
The most commonly used method for meditating could not be simpler to do. You simply sit on the floor with your legs crossed (or sit in a chair, or lay down, depending on what is comfortable), and then quiet yourself and remain there. This will feel incredibly unnatural at first. You will likely experience an urge to move around, to scratch, or to get up and do something. You may even experience some anxiety. This is okay. The nature of the task is to simply observe these urges and sensations as they occur, and then to let them go when they are no longer urgent. Don't act on these urges, but instead simply observe them. A variety of thoughts and feelings will parade through your mind making their usual demands; your task is to observe them rather than to respond to them. Hold on to nothing; just watch. If you get distracted and start acting on an urge, just note that this occurred and go back to your watching. Sit there and observe for 20 or so minutes (set a timer so you don't have to watch the clock - which will kill the experience). When the timer goes off, get up and go about your business.
Meditation is not something that will pay off quickly. In fact, it will take quite a long time of regular practice before you will "get it" and start feeling the benefits it has to offer. Practice meditating every day at a regular time, for a regular duration. Remain alert during your practice; do not go to sleep! Be patient. Ultimately, your perspective will start to evolve and you will grow more able to choose your moods and reactions instead of them choosing you. Meditation practitioners typically report feeling much calmer than they did prior to meditation, and much more focused and clear-minded. The stressful things that used to distract and torture them fall away.
More information on meditation is available here.