About 10 years ago display manufacturers found that using a glossy or smooth finish on the screen (usually on a plastic cover over the actual glass) rather than the previous matte (many tiny bumps) finish resulted in an apparently greater level of contrast. That is, blacks looked blacker, whites were whiter. The trade-off was that these glossy screens are much more reflective than the matte finishes.
Think of it like a mirror. A good mirror will have a very smooth surface, in fact, all the components of a mirror are very smooth to order to reflect images in them accurately. If you ran sand paper over the mirror, making the surface bumpy, you'd, in effect, have a matte finish. Anything reflected in the mirror would be dispersed a little bit rather than being reflected directly to your eyes in the way they appear "normally". This would result in a fuzzy or slightly blurred image because small parts of it are being reflected off somewhere other than to your eyes.
When applied to LCD screens, a glossy finish results in much clearer reflectivity, just like a good mirror. Whether you like it or not, or whether you can adjust to it or not is entirely a matter of preference.
Personally, I prefer the glossy screens. The image appear to me to be clearer, especially when gaming or watching movies. However, the more clear reflections do bother people I know, and so they tend to use matte-finish screens.
It's entirely up to you.
If you're in a work environment, see if you can find out of someone else would trade you their matte screen for your glossy.
UPDATE with info on anti-glare:
Antiglare can be both the simple method of a matte finish, or it can be coatings and glass quality levels. Glass reflects a little bit, even without a reflective surface adhered to it (like a mirror), this is primarly due to impurities on the surface of the glass. A freshly cleaned window will reflect less than a dirty one (though, ironically, the cleanness of the glass will also make what reflections it does create more clear), but it takes very special types of glass or special coatings to cut down on the natural reflectivity of glass.
When you look at someone's glasses, you can usually actually see the glass, even though both you and I would still say the glass was "clear". There are higher-end glasses that are so clear it can be difficult to actually see the glass in the glasses. If this glass were used in the manufacture of screens, it could have the benefits of a glossy screen high-contrast screen such as I prefer, without the headaches of strong reflections that cause many people to prefer the matte finish.
I'm not aware of screens that do this yet, as normal glass is more than adequate for most people, and a matte finish dimishes the clarity of the image so little as to be negligible.
