The rate of a reaction depends on the concentration of reactants, we can write the rate as proportional to the concentrations to some power, for the reaction of A with B
aA + bB ---> products
rate ∝ [A]
abYou can always make a proportionality into en equality by adding a proportionality constant k.
rate = k[A]
abThis proportionality constant k is the rate constant, that's all the rate constant is, a constant of proportionality.
Arrhenius simply noticed that, if you change the temperature of a reaction, the rate changes, so the rate equation must have some Temperature dependence!
[A] and
don't have a temperature dependance (we can choose initial concentration whatever temperature) so the temperature dependance must be contained in side the rate constant.
This means that the rate constant isn't actually constant! It depends on temperature!
The Arrhenius equation is simply the suggestion that arrhenius made as to how the rate constant might depend on temperature (he wasn't just guessing, statistical methods beyond this level give you the Arrhenius equation)
So, to conclude, the rate constant is simply something introduced so we can express the rate in terms of concentrations and the Arrhenius equation is simply a model of how rate changes with temperature and how the rate constant k can be written to accomodate the temperature dependence!
This has an a-level description of rate constants, give it a read (chemguide tends to have good explanations of most topics at a level)
http://www.chemguide.co.uk/physical/basicrates/orders.html