Why do some labels say that a wine is unfiltered? Is that a boast or a warning?
It's a boast. And, no, it doesn't necessarily mean you'll find unsightly sediment in the bottle.
Many producers feel – quite rightly, I believe – that filtering can strip wine of subtle flavours. You generally want to filter for one reason, to remove haze and make the wine sparkle. Wine can contain many insoluble ingredients, such as proteins, tartrates, tannins and yeast cells. Over time, these will precipitate out of solution to form sediment.
That's why you may wish to decant a very old bottle, separating the liquid from the particles. Be careful to keep the bottle upright for a few hours (preferably eight or more) prior to uncorking an old wine so that the sediment has a chance to fall to the bottom. Then pour slowly and leave the last ounce or so in the bottle, which you can discard. Sediment is harmless, by the way, but it can render the drinking experience unpleasant. I know a sommelier who actually likes to collect sediment from old bottles of port and spread it on toast with blue cheese. It's a testament to the fact that there's flavour in the solids.
With a young wine, though, chances are you won't notice the particles because they'll be suspended evenly in the liquid.
The word "unfiltered" on a label is just a way for a winery to telegraph its commitment to minimal intervention, a hallmark of many great wines.