What is curve fitting and how do I fit a curve? I want to understand the concept. What material could I read to learn about it?
 A: Marcio, here is a simple try before you go into all sorts of scientific stories.
Let's fit a "curve" called a line through two given points: (1,1) and (2,2)
Perhaps you realize that the best line is y = x right? It's the best fit.
Now there is a third point coming in: (4,5) Obviously there is no single line passing through all three points. The question then becomes: Is there a line that "deviates the least" from these three points? In other words, can you construct a line that passes these three points "as close as" possible? It is almost like a game who can draw such a line the best. This is in lay man's terms "curve fitting", because the scenario I described with a line and three points, can be extended to a polynomial with many points... 
A: I don't think this has to do with geometry. Curve fitting is creating a curve (e.g. a line) that best describes a certain set of data.
http://en.wikipedia.org/wiki/Curve_fitting
Like here:
http://en.wikipedia.org/wiki/File:Regression_circulaire_coope_arc_de_cercle.svg
You might want to check out linear regression (curve in question is a line). Ch11 I think here: http://ihmsi.org/upload/Richard%20J.%20Larsen%20-%20An%20Introduction%20to%20Mathematical%20Statistics%20and%20Its%20Applications%20-%205th%20Edition.pdf
Or for other curves: http://kau.edu.sa/GetFile.aspx?id=188051&fn=Larson%20-%20Edwards%20y%20Falvo%20Elementary%20Linear%20Algebra.pdf
