What Does 'Zero Order Hold' and 'First Order Hold' Mean?
We need to assume the reader knows some basic stuff to answer that.
Let's give it a try.

Lets understand the sentence - Zero / First Order Hold.
We have the Zero / First Order and the Hold.

Zero / First Order hold means the order of the Taylor Series of the function we use to interpolate. In other words, the degree of the Polynomial we can write the function with.
Zero Order means the function is constant, we interpolate the same value in the missing parts.
First order means we can use linear function to interpolate (Line with a slope).  

Hold means we hold the parameters to be the same until the next sample.