In Buddhism the person meditating is not trying to get into a hypnotic state or contact angels or any other supernatural entity. Meditation involves the body and the mind. the Buddha said 'All that we are is the result of what we have thought: it is founded on our thoughts, it is made up of our thoughts'. (Dhammapada Chapter 1:1-2). For Buddhists this is particularly important as they want to avoid what they call 'duality' and so their way of meditating must involve the body and the mind as a single entity.
In the most general definition, meditation is a way of taking control of the mind so that it becomes peaceful and focused, and the meditator becomes more aware. The purpose of meditation is to stop the mind rushing about in an aimless (or even a purposeful) stream of thoughts. People often say that the aim of meditation is to still the mind. In Buddhist tradition, meditation is the second part of the 'threefold path'. There are many formulations of the Buddhist path to spiritual awakening but the threefold path is generally seen as the most basic one. The first training, and the indispensable basis for spiritual development, according to the Buddha, is ethics (shila). Buddhism does not have laws or commandments but its five ethical precepts are guidelines for how to live in a way that avoids harming others or oneself. Meditation (samadhi) is the second training. Acting ethically gives rise to a simpler life and a clear conscience, which are a sound basis for meditation practice. Meditation clarifies and concentrates the mind in preparation for the third training: developing wisdom (prajna). The real aim of all Buddhist practice is to understand the true nature of our lives and experience.
There are a number of methods of meditating - methods which have been used for a long time and have been shown to work. People can meditate on their own or in groups. Meditating in a group - perhaps at a retreat called a sesshin or in a meditation room or zendo - has the benefit of reminding a person that they are both part of a larger Buddhist community, and part of the larger community of beings of every species. In the tantric Buddhism of Tibet and elsewhere, meditators visualise complex images of Buddha forms and recite sacred sounds or mantras (in fact these images and sounds have significance beyond simply being objects of concentration). The most common and basic object of concentrative meditation is to focus on the naturally calming physical process of the breath. In the 'mindfulness of breathing', one settles the mind through attending to the sensations of breathing. In zazen or 'just sitting' practice from the Japanese Zen tradition, one sits calmly, aware of what is happening in one's experience without judging, fantasising or trying to change things.