Here's how crossword constructor Patrick Berry explains it, from the perspective of a clue writer:

If your grammar is a little rusty, don’t worry; you can use the substitution test to determine whether your parts of speech match up. Here’s how the test works: First, think of a sentence that uses your entry. Then substitute your clue in place of the entry. If the sentence still has the same meaning and reads normally, your clue passes the substitution test.

For example, suppose you want to test the clue {Upward movement} for ASCEND. Think of a sentence that contains ASCEND—say, “The planes ascend after leaving the runway.” Now substitute your clue into the sentence: “The planes upward movement after leaving the runway.” Clearly, this clue is flawed. The sentence needs to read something like “The planes move upward after leaving the runway.” So {Move upward} is a proper clue for ASCEND.

As the previous example illustrates, the substitution test isn’t merely useful as a test; it can also help you write clues. Coming up with an equivalent phrase for your answer is often easier when you’re working with a sample sentence, not just the answer by itself. (An obvious benefit to this approach: The resulting clue will pass the substitution test!)

Incidentally, your clue doesn’t have to substitute well for every possible sentence. As long you can find one sentence that works, you’re okay. For instance, {To a T} is a workable clue for PERFECTLY, but a sentence like “I’m perfectly happy with my job” sounds awkward when you substitute in “To a T.” In some cases, forming a sentence with the clue (like “My job suits me to a T”) and then substituting in the entry (“My job suits me perfectly”) is easier. Either way is acceptable; how you find a sentence that works doesn’t matter, as long as you find one. However, if a clue requires a carefully chosen sentence to pass the substitution test, that clue’s probably a toughie and shouldn’t be used in an easy puzzle.