What is the reaction order of a reaction?
Very Shortly, Rate of reaction is directly proportional to product of the active masses of reactants raised to some power which is Order of the Reaction.

Consider an elementry chemical reaction
$$\ce{2A(g) + B(s) -&gt; C }$$ 
As reaction is elementry, stoichiometric coefficient and order will be same. The order of the reaction will be 2 (as the other component is solid, therefore will not affect concentrations). The rate law for reaction will be given as 
$${R = K[A]^2}$$ 
where K is reaction constant.
[A] is concentration of A.
If the order of the reaction would be 0, then Rate would be equal to reaction constant itself as the rate law would be given as 
$${R = K[A]^0}$$ 

This explains the maximum use of Order of the reaction and also what order of reaction is. 
Edit: for more wide explaination on this, see wikipedia. (Same explaination is provided but a widely expanded.)