"Parse, don't validate" is an approach to modeling data such that it is impossible to construct without verifying the integrity of the data first. Thus when using such data, one can be sure that it is already in the correct shape and no further validation is necessary.
In short, this approach makes it explicit where your data gets refined. This blog by Alexis King uses examples in Haskell, mostly because the language has a short and concise syntax. To show that such an approach works in any other language too (albeit with a bit more boilerplate approach), Jan will also demonstrate it in Java.