Tonic... Dominant... Help?

"How can you compose without knowing that??" --Heard that one being asked a lot, and now i ask myself the same. 

Basically, i've skipped that one when i used to do music class some years ago, and i am getting myself stuck all the time when trying to compose melodies/chord progressions that make sense. 

So, what exactly are tonic, dominant, etc chords? What is their purpose? Why are they even called like that? Which are their practical aplications? How did composers use it? Is there such a thing as a dominant, tonic etc note (yes note, not chord).

While it would be possible to give a superficial answer to your question (e.g., tonic and dominant chords are the chords built on the first and fifth degrees of the scale; in C major, which is CDEFGABC, they are C and G) as well as unsystematic and therefore near-useless information (these chords are primarily used in cadences, with V followed by I constituting a full cadence which completely closes a unit, and a stop on V constituting a half cadence which leaves a unit open for continuation), you need to invest some time (and maybe money) in a good book and/or teacher for the concepts to be of any use.

I think when you were asked "How can you compose without knowing that?", this wasn't referring to a specific piece of information, but to the fact that an unfamiliarity with these concepts implies a complete unfamiliarity with the system of tonality, and theory of composition, which rests on them.

The question demands an answer which requires more in depth of an answer than this medium affords.

In short, everything. A millenium of music can be summed up as an exploration of the tonic dominant interchange.

If you wish to contact me directly we can speak more in depth.

There's a little chart here with the different names.  You can learn to sing with Do, Re, Mi, Fa, So, La, Ti, Do.  But when talking about music theory and composing we refer to the same steps in the scale as Tonic, Supertonic, Mediant, etc…  Tonic = Do.  The first note in any scale and the note that you inevitably keep coming back to to make a tune feel finished and resolved.  It's also the name for the chord built on that note.  So a tonic triad in the key of C major is built on C, the first note in a C major scale.  So it is a triad that goes CEG.  In any major scale the tonic triad is always a major chord, because of the arrangements of whole steps and half steps in a major scale.  The Supertonic (Re, 2nd step in the scale) triad in a major key turns out to be a minor chord.  (DFA in the key of C major).  The patterns of which chords are major or minor or diminished is part of what makes ear know you are in a major or minor key without you knowing any music theory.  We all just naturally hear it and respond to it emotionally to feel happy and major, or sad and minor.  And we intuitively write things that have a lot of tonic chords in them and a lot of dominant chords in them.  That is part of what tells our ears what key we're in, so that a piece doesn't feel like it is wandering around aimlessly.  There's a lot of theory about how best to do that, and why our ears respond in certain ways, but the fact is we DO respond, without thinking about it, so composers tend to write that way, without thinking about it.  

i found that modern music generally avoids the dominant-tonic relation. it's too "childish". the plagal cadence is more typically used. ( subdominant-tonic / IV-I)

I don't understand why you think something you'll read here will be more informative than the dozens of authoritative texts on the subject.

People have been answering this question for hundreds of years. People who understand the concept much more thoroughly than anyone here.

Schoenberg:

http://www.amazon.com/Structural-Functions-Harmony-Revised-Edition/dp/0393004783/

http://www.amazon.com/Theory-Harmony-Arnold-Schoenberg/dp/0520266080/

Piston:

http://www.amazon.com/Harmony-Fifth-Edition-Walter-Piston/dp/0393954803

Tchaikovsky:

http://www.amazon.com/Guide-Practical-Study-Harmony-Dover/dp/0486442721

Rimsky-Korsakov:

http://www.amazon.com/Practical-Manual-Harmony-Nikolai-Rimsky-Korsakov/dp/082585699X