Excess & Limiting reactant

Excess quantity: In real chemical reactions, it is necessary to add more of the reactan than the equation predicts because it is not possible for every atom/molecular of reactants to come together.
One reactant is the excess quantity and some of it will be left over. The second reactant is used up completely.

When dealing with this kind of problems, having a correctly balanced equation is always important.
Because it will give a prediction and with that, you can find how much chemical left.
Example: Which chemical will left when 20g Mg react with 10g HCl and how much will left?
First, give a correctly balanced equation: Mg +2 HCl == MgCl2 + H2
1 mol Mg can make 1 mol H2;
2 mol HCl can make 1 mol H2.
20g/(24.3g/mol)*(1 mol H2/ 1 mol Mg) = 0.82 mol H2 = 1.64g H2
10g/(36.5g/mol)*(1 mol H2/2 mol HCl) = 0.14 mol H2=  0.28g H2
 At that time, we can clearly see that 20g Mg can make more H2, so that Mg will be left and O2 is going to be used up.
But how much Mg will left?
0.14 mol H2 * (1 mol Mg/ 1 mol H2) * 24.3g/mol = 3.4g 
20g-3.4g = 16.6 g Mg left