great answer from spo1997. i'll add a bit more info.
the idea behind decanting is to expose the wine to air, which encourages the fruit aromas and flavors to open up (which is dandy, if it's a complex young wine that's meant to be aged). as the fruit opens and becomes more pronounced, the tannins seem less astringent though they don't actually decrease.
after a while (a couple hours to a couple days, depending on the wine), the fruit starts to fade; it can only take so much air. as the fruit fades, the tannins become more prominent. eventually, all the fruit will fade and the wine will be dried out and tannic.
in a decanter, the amount of tannin stays the same; it's basically the power of the fruit that varies. tannins take much longer to polymerize and evolve; this requires years in barrel or bottle.
looking at it in another way, wine is an intricate balance between its soft components (fruit, sweetness, alcohol) and its hard components (acidity and tannin). by decanting, you're boosting the fruit, which is soft, so the wine seems more soft, less hard.