There are some different applications.
For one, it tells you how many times an acid can lose a proton. For instance you can have a diprotic ("with 2 H+") molecule, with n=2. For instance, H2SO4, deprotonates to HSO4-, which can then go to SO4(-2).
Why is that important? Take an acidic reaction with H2SO4. If the extent of reaction is strongly forward, you would treat H2SO4 as if it had twice its concentration to take into account that it has two protons it can lose. If you only accounted for the first proton you would be underestimating this effect.
It's also known as equivalent concentration, which might make it sound less foreign to you.
In redox reactions, it shows how many electrons an agent can accept/donate, and in precipitation reactions it measures the # of ions that'll precipitate out of a solution. For all these situations the n-factor or equivalent concentration corrects for multiplicity, since now we know not all molecules are made equal. Some acids can deprotonate twice, some reagents will lose 4 electrons in redox while others may lose just 2. To consider these differences we use this concept.