What is non standard measurement?

Answer 1

Using a non-standard scale.

Science has generally agreed on a bunch of units grams, meters, joules etc to make up the "System International" or SI units. These should be used in a scientific context. They are based on Standards - for instance there used to be a stick in Paris which was defined as being a meter long all other meters had to be that length. They now use some trick with wavelengths of red light. Back on topic -

There are other scales in general use mostly for historic reasons. The "customary units" in the US for distance (miles, yards, feet and inches) and weights (Pounds and Ounces) being pretty common examples. Using these scales could be considered nonstandard if you were writing a scientific paper.

More likely nonstandard measure would be using a scale that is no ones standard. I could (and have) built a scaffold structure using units of "Rebecca" a nice girl who happens to be a good length to put scaffold floors apart. But I think you would have to consider her a nonstandard measure. The point being if you use nonstandard measure then people are not going to understand you since there is no common reference or "standard" to compare to.