Primary and secondary standard
A primary standard is critical for an analytical result. If we dissolve a known mass of a material into a known volume, we must be able to know its concentration with confidence. Such a standard must be easily made very pure (> 99.95%), it should not decompose, and it must be fairly robust to say heating or vacuum. We use such standard solutions as, for example, titrants. This is surprisingly hard to come by, and so we say that secondary standards are materials that do not meet these strict criteria.

Say you want to titrate a sulfuric acid solution for quantitative work, you could use a known concentration of NaOH or KOH and volumetrically determine the concentration of the sulfuric acid solution. In fact, dissolving pellets of these particular bases in a known volume of water is not sufficient to calculate concentration with any confidence in analytical work because the solids are contaminated with carbonate from atmospheric CO$_2$. In general these carbonates contaminate alkaline solutions quite readily through this reaction: $\ce{OH- + CO2 -&gt; HCO3-}.$ This is why we would have to titrate the concentration of $\ce{NaOH} $ solution with a primary standard before using it as a secondary standard.

Now there are acid and base primary standards available, so why would one ever need to use a secondary standard? Usually it’s a matter of specific needs and convenience. Whenever possible, use a primary standard if your results actually matter.

Let us look at a specific case where a secondary standard is useful: potassium permanganate is exceptionally useful as a titrant because it serves as its own indicator where the presence of a purple color signifies the end point, but it is unstable in light or heat due to this reaction: $\ce{4 MnO4^- +2H2O -&gt; 4MnO2 + 3O2 + 4OH-}$. This is why solutions of it must be stored in a dark cool place; even still, we must standardize the concentration of such a solution and we can only trust its measured concentration for a short time thereafter.

A secondary standard solution of $\ce{KMnO4}$ is usually titrated by oxalic acid, a primary standard, and then used to determine the concentration of a number of other analytes.

The reaction with oxalic acid can be summarized as $\ce{5 H2C2O4 + 2 MnO4- + 6H+ -&gt; 10CO2 + 2 Mn^{2+} + 8H2O}$ where everything except $\ce{MnO4-}$ is colorless. The end point of this titration is a marked by a purple color due to unconsumed $\ce{MnO4-}$. This allows you to make a standardized solution of potassium permanganate that can be used for a short while.

Now, how would we use this? Solutions containing $\ce{Ca^2+, Pb^2+, Ag+, Mg^2+, Co^2+, Zn^2+}$ and etc. can be precipitated as a metal oxalate. You would then digest this ppt in an acidic solution and titrate the released $\ce{H2C2O4}$, where the end point is marked by a purple color, allowing you to infer the original concentration of the metal ion in the original solution.

$\ce{KMnO4}$ was used in mineralogical surveys of uranium prior to the Manhattan project, where better techniques were developed to quantitate.