I just found "Robust Fitting of Linear Models" rlm() function in the MASS library.
I would like to know what is the difference between this function and the standard lm() (linear regression).
Could someone give me a short explanation?
It is for robust linear models. It is describe in Venables & Ripley. However, details of the robust calculations would not fit in a "short answer": you need to look into several papers by Ripley, Tukey, and others.
Check out this paper by Ripley for more information: http://www.stats.ox.ac.uk/pub/StatMeth/Robust.pdf