When you start filling in words in a difficult crossword puzzle, you're not very certain about your guesses. They're often far apart from each other. Some of them are more tentative than others. But once you take them, tentatively, for granted, you can start guessing harder, longer words.
Sometimes you just can't make sense of a longer word's clue with the words you have down. This is evidence that some of the words you've chosen are wrong. They don't work. But sometimes, harder clues just answer themselves --- this is evidence in favor of the words that you've already put down.
It supports itself. Each new word is evidence to evaluate earlier words. As you continue to fill in words, your confidence in the earlier words grows. You're never 100% certain that you've got them right (even after you're done -- what if you have stumbled upon a perfectly consistent but wrong solution to the clues?) but you're close enough that it's not worthwhile to waste time qualifying "I got the crossword!" with "(except in the the improbable, but not quite zero-chance, case that I happened upon a self-consistent solution to all of the clues which is not correct)."
Science is the same way. New discoveries don't happen independently of old discoveries; they're assisted and informed by old discoveries. We have to re-evaluate those old discoveries in light of the new discoveries, the old theories in light of new theories, and the old observations in light of the new observations.
A crossword puzzle is not a perfect analogy. Scientifically, many observations (the "clues" in the puzzle) rely on existing theory ("words"). Imagine a crossword puzzle with almost all of the clues embedded in the puzzle itself, and you're getting somewhere. But it's good enough to illustrate the point that science isn't many independent observations all pointing at some abstract "truth" - it's a series of interlocking theories, each of which is evaluated in light of each other.