In Matthew 6:27, Jesus poses the rhetorical question, "Who of you by worrying can add a single hour to his life?" A least, that's how the NIV translates it. Look a little further, though, and you will see a footnote offering an alternate translation: "Who of you by worrying can add a single cubit to his height?"
These two translations seem significantly different. How is it possible that the Greek can be translated both ways, and which is the better rendering? Well, the simple fact is, the word for life used here is helikia, and this word really can refer either to the length of a person's life (or a portion of it) or to a persons stature. And where the NIV says "an hour," the Greek word is pechus, which means a length as in a length of string. How long is a piece of string? It's just as long as it is. Pechus is no more specific than that. So, if the subject is a lifetime, an hour is a reasonable span to use in the translation, as would be a day or a year or any other measurement of time. Likewise, if the subject is a person's stature, a cubit, an inch, or a millimeter would all be reasonable similes.
But here's the thing, in context, ether translation works. Or rather, both translations work. This sentence, in the Greek, is a fantastic double entendre. It refers backward to the preceding verses, which talk about fear over the the basics of sustaining life, having food to eat, and it introduces the following verses about vanity, the need to look good or impressive. In fact, in the latter case, it plays a double meaning again. The illustration of grass is a common Old Testament metaphor for the brevity of life. So worrying about how long you will live applies here, too.
As nice as this word play is, the need for an application remains. After all, the Bible does not exist to inform us alone. The informing should lead to transforming. So, what's the application here?
For me, the biggest value is in what it tells me about the Bible in general, and the Gospel of Matthew in particular, and more specifically, the Sermon on the Mount itself. These are not words thrown carelessly together, not "random thoughts by Jesus," as I once suspected them to be. I read one commentary that suggested the latter half of the Sermon on the Mount consisted of all the teachings Matthew could not logically fit anywhere else. I strongly disagree with that idea. The closer one looks, the more one finds evidence of meticulous care by the author. In some cases, this precision seems to reach beyond the capabilities of man and suggest divine direction. An example of that can be seen in a (slightly cheesy) video titled "The Bible, Pi & Logarithms - Supernatural Design II."
So, the general application here is theological. Is there, then, a more direct application. Indeed there is, and it has to do with both possible meanings of the verse. The application is simple this: Get a grip. Life is short. Don't waste it worrying about things that will die when you do. Focus on what really matters, seeking God's rule in your life.