These is no easy way to answer these questions. There are many types of meditation, many schools, methods, and teachers. Their corresponding goals may vary significantly.

As defined on the Wikipedia meditation page:

Meditation describes a state of concentrated attention on some object of thought or awareness. It usually involves turning the attention inward to a single point of reference.

This is really not so bad a definition, as it comprises the essential point of employing your ability of focusing on some object. In many types of meditation your awareness will be focused on our own being, either on some specific area of your body, on a specific process taking place within your body (breathing), on mentally repeating some words (mantras), or for instance on some sort of visualization.

There is a sea of meditation techniques. What kind of meditation you are going to engage yourself is a question of attraction, level of spiritual achievement, strength of your desire to explore your own universe, and other factors.

For example, you can try various types of guided meditation, or transcendental meditation - quite popular in the western world, you can follow the ancient schools of Buddhist meditation, or you you can engage yourself in practicing some techniques of meditation that are more suitable and adjusted for the contemporary era we are living in.

If you are a beginner you can also find some tips on how to meditate for beginners.

But the most important advice is this: if you are in doubt listen to your heart first. But, it does not mean that you should totally discard your mind while doing that.

Regardless of the type of meditation you are practicing, if you are open minded, free-thinking spirit, the meditation exercise should help you expand your consciousness and make you realize the truth about your own being - your true character, your behavior patterns, your relationship patterns - and also help you start getting rid of your illusions.This is the crucial point. These are the real benefits.

Do not allow yourself to be guided by the desire for powers or control of any kind. Set your goals high, much higher that that.

Yes, practicing meditation can naturally bring you many improvements, for instance, increase your general health, but the bottom line is this - it should enable action toward personal growth and improving your knowledge, awareness, relations to others, and self-realization.

Keep in mind that very often less is more. You would like to liberate yourself, your being, not to make it a slave to just another thing.

Still a word of caution to the beginners. It is often a good advice to find an experienced teacher or meditation instructor if you are just starting with meditation.

If you want to preserve your current state of being and functioning, if you do not want to change yourself, practicing meditation can still help you achieve better life and more serene state of mind, but the full power of diving into your own Divine nature will not be employed.

The ultimate goal of any type of meditation should be attaining a state of consciousness which is often being called enlightenment. Enlightenment is only a different expression for the direct experience of the Truth.

The enlightenment can be shallow of deep, it can be only an insight or really a profound experience. It does not really matter because each enlightenment is immensely valuable.

The enlightenment is the most valuable gift one can have in one's life.

If you were to extract the essence of the true meditation and forget about the forms, rituals, and cultural and traditional background, you wouldn't be able to distinguish it from a true prayer. In meditation as well as in prayer you are addressing your Divine Self - with words or without - it doesn't really matter.