In a chemical reaction, the limiting reactant is the species which is in lowest stoichiometric quantity. In other words, it is the reactant which is consumed before any others.
Take the chemical reaction
Say you have equimolar quantities of hydrogen (H2) and oxygen (O2). Since 2 moles of hydrogen are required for every 1 mole of oxygen, when all the hydrogen is used up there is still leftover oxygen. Thus, hydrogen is the limiting reactant, because it is used up first.