I kinda know it(thanks to Wikipedia), but I'd like to know if there's a (text)book that would explain it to me. ADDED: I'd rather prefer to see the theory of modular forms developed from the more abstract point of view. I mean, I'm working them already from the elementary textbook of Apostol, after skipping through Koblitz's book and a chapter in Serre's "Arithmetics," but I would like to get more motivation as to how they are connected with more general, hardcore stuff. By this point of time, I have kinda satisfied my initial desire to learn about curves that are also tori(OMG! how can a curve be also a torus?)
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A lot of people learned this material from Katz's article $p$-adic properties of modular forms and modular schemes (especially the material at the beginning of the article), in Lecture Notes in Math 350. This article presumes familiarity with algebraic geometry in the language of schemes, though.
If you want material that is more advanced than Serre's course in arithmetic, but is not as advanced as Katz's article, you could try reading the various survey papers of Ogg from the early 70s (easily found on MathSciNet). In these articles he explains how modular curves parameterize elliptic curves with certain kinds of prescribed torsion data, and in particular formulates his famous conjecture, proved by Mazur not long thereafter, to the effect that the only possible orders of a torsion point on an elliptic curve over $\mathbb Q$ are $1,\ldots,10,$ and $12$.
Another good thing to read is this expository article of Tom Weston, in which he gives explicit descriptions of the modular curves $X_0(11)$ and $X_1(11)$, explains their moduli-theoretic interpretation, uses modular forms to find explicit equations for them, and so on. It would serve as an excellent complement to Ogg's articles.
If you want to go further than what is to be found in these expository articles, the natural next steps will be to study Silverman's two books on elliptic curves, and to learn more algebraic geometry (so as to be able to read Katz's article, or analogous articles).