What a great topic for discussion!
I'll do my best to explain meditation, as I understand it, from a yogic perspective, where (as was mentioned above) Meditation (dhyana) differs from contemplation and concentration (dharana).
Looking at what Patanjali's Yoga Sutra has to say, the last four rungs/steps/limbs of Ashtanga Yoga ("the eightfold path") are prathyahara (sense withdrawl), dharana (concentration), dhyana (meditation) and Samadhi (absorbtion--and it should be noted that there are different levels of Samadhi).
As I understand it, one can't just say "OK, I'm going to practice pratyahara now," but rather pratyahara itself naturally arises as a result of something else, sitting still and closing your eyes is not itself pratyahara, but pratyahara may arise as a result of sitting still and closing your eyes, and then beginning to focus on the breath, a mantra, etc....at some point you turn inward. The senses are no longer pulling you outward. (If any Yogini's can expand upon this please do!)
As far as the last three steps are concerned, first of all, an object of meditation must be chosen-- (Interestingly enough, unlike in English, the Sanskrit root meaning "to meditate"--dhyai, is actually a transitive verb, so literally, it's more like "to meditate on.") this could be the breath, a mantra (sacred word(s) or sound(s)), diety, yantra (sacred geometric diagrams), candle flame, religious symbol, etc.
The limb that follows pratyahara--dharana--is about concentration, focusing on the object you've chosen--but it is not meditation.
And focus is hard! There's a constant back and forth--the mind wanders, and then it comes back to the object, then it wanders again, etc. focusing takes effort!
But maybe, eventually, we come to a place where it becomes effortless--there's an effortless, conscious flow between you and the object; in other words a connection! That's meditation--dhyana.
There's no longer this "struggle" to come back to the object that you were concentrating on--it's effortless.
And there's a connection-- direct communication--between the meditator and the object of meditation
it's no longer "The object and I" but rather, "The object and I and our communication--our connection."
During true meditation, the object actually transmits it's qualities on to you (which is why meditation can lead to such powerful transformation). So there's this mutual communication and if you look at
the etymology, the root of the word dhyana is dhi--which means "intelligence"--an awareness of this communication, and the intelligence--those qualities imparted to you by the object of meditation.
And then finally, Samadhi--absorbtion (literally, sama=same--aren't English/Sanskrit cognates cool?, dhi=intelligence; so it's this realization--more so than just an intellectual understanding, but true, experiential knowledge--of the oneness between the meditator and the object of meditation.--you experience oneness with the object of meditation.
Though is isn't exactly a complete definition-- as I said, there are different levels of Samadhi--Sutras 1.17 and 1.18 discusses this in more detail (Swami Satyananda Saraswati offers an excellent commentary elaborating on this in "Four Chapters on Freedom," his translation of the "Yoga Sutra."...I don't want to go any more off-topic than I already have :)
A really "concrete" explanation, definition is given in the translation and Commentary on the YS by Swami Prabhavananda and Christopher Isherwood--to paraphrase, they say that if the mind is able to focus on the chosen object for 12 seconds--that can rightly be called "concentration," if this is continued for 12 times 12 seconds, that's meditation, If the meditation is continued for 12 time that amount of time, that will result in the lower form of samadhi and if the lower samadhi can be maintained for 12 time that amount of time, then that will result in the highest level samdahi.
But..though the above is a very "linear" explanation, the interesting thing is, it's not like it's totally linear, it's a constant process--a constant fluctuation--like a dance in a way, you might touch samadhi and then slip back to meditation, and then concentration, and then back to meditation again, etc.