My main example was working with a co-worker whose application used a number of timestamps. They were passing them around as strings and parsing and doing math with them at the point of usage. But, by parsing the inputs into the language's timestamp representation, their internal interfaces were much cleaner and their purpose was much more obvious since that math could be exposed at the invocation and not the function logic, and thus necessarily, through complex function names.
If you instead parse the data (which includes a validation step) and produce a Maybe NonEmpty, if the result is a Just NonEmpty (vs Nothing) you can pass around the NonEmpty result to all the calls and no more validation ever needs to occur in the code from that point on, and you obviously reject it rather than continue if the result is Nothing. Once you have a NonEmpty result, you have a proof (the type itself) that is carried with it in the rest of the program.
This types-are-propositions persoective is called the Curry-Howard correspondence, and it relates to constructive mathematics (wherein all proofs must provide an algorithm for finding a "witness" object satisfying the desired property).
validateNonEmpty :: [a] -> IO ()
validateNonEmpty (_:_) = pure ()
validateNonEmpty [] = throwIO $ userError "list cannot be empty"
parseNonEmpty :: [a] -> IO (NonEmpty a)
parseNonEmpty (x:xs) = pure (x:|xs)
parseNonEmpty [] = throwIO $ userError "list cannot be empty"
Both consolidate all the invariants about your data; in this example there is only one invariant but I think you can get the point. The key difference between the "validate" and "parse" versions is that the structure of `NonEmpty` carries the proof that the list is not empty. Unlike the ordinary linked list, by definition you cannot have a nil value in a `NonEmpty` and you can know this statically anywhere further down the call stack.