What is too obvious to explain in a scientific paper? Recently I had my paper reviewed for potential publishing. With no big surprise I need to make some adjustments to my paper. One of the criticisms was that my work lacks "textbook explanations" (e.g. what is BETA, alpha). 

To further clarify, this is the first ever work I ever plan to get published  (academic context is finance). But I am surprised I should be required to explain basic concepts.

Would you have any recommendations as to what is the best way to incorporate these explanations in a work (e.g. footnotes) and what should be explained (of this really basic stuff/how to identify it) and what not?
Symbolic notation must always be defined in a paper.  The reason is that there are not that many symbols and lots of things they can be used to represent.  Thus, even if every class you ever took used v to represent voltage, other people are using it to represent velocity, vertices, values, etc.  See, for example, this far-from-complete Wikipedia list of how Greek letters are used.

At a minimum, each symbol should be defined the first time that it is used.  It is also helpful to your readers to provide a table of important symbols and to refresh their memory on definitions of critical symbols from time to time.  This can often be done quite simply and efficiently within the sentence where the symbol is used, e.g.:


  we consider a particle traveling at velocity v through a magnetic field of strength B(x), where x is the position of the particle in space.