The reactant which is present in the least amount gets consumed after some time and after that further reaction does not take place whatever the amount of the other reactant.
Hence, the reactant, which gets consumed first, limits the amount of product formed and is, therefore, called the limiting reactant.
Example
In the reaction given above, 3 moles of Hydrogen gas are required to react with 1 mole of nitrogen gas to form 2 moles of ammonia.
But what if, during the reaction, only 2 moles of hydrogen gas are available along with 1 mole of nitrogen.
In that case, the entire quantity of nitrogen cannot be used (because the entirety of nitrogen requires 3 moles of hydrogen gas to react). Hence, the hydrogen gas is limiting the reaction and is therefore called the limiting reagent for this reaction.