What is induction exactly?

What is it about induction that you struggle with? Also, do you mean electromagnetic induction, where a varying magnetic field generate a potential difference in a conductor or electrostatic induction as in the operation of a Van der Graaf generator?

 

What don't you understand about it? Have you read the wikipedia or hyperphysics articles?

 

There are plenty of good articles online that explain what induction is. We can't really help you unless you ask some specific questions.

Electromagnetic induction. It's in post #3.

 

The Wikipedia article (at least the one in the English Wikipedia) is very good. Unfortunately there are many sources (even textbooks) which add a lot to the confusion by stating the law in integral form but are not carful enough with the time derivatives. That leads to all kind of confusion. This confusion has a long tradition. It's as old as the discovery of induction by Faraday. The good thing about this confusion is that it lead Einstein to the clue, how to solve the problem how to describe electromagnetism in different inertial frames, which lead to the famous paper "On electrodynamics of moving bodies" (translation mine), i.e., the final formulation of what we call Special Relativity Theory today.

In the Wikipedia the derivation of the integral form of the induction law from the fundamental (local) laws is correct. When you use this complete formula, there shouldn't be any confusion:

http://en.wikipedia.org/wiki/Faraday's_law_of_induction#Proof_of_Faraday.27s_law