When it comes to choosing binoculars you can get confused unless you happen to work in optics or have a good handle on optical physics! All the lingo and terminology can be confusing and there are so many binocular brands to choose from now too. It need not be so confusing, read through this little overview or read on at the links below to arm yourself with the understanding you need.
The first thing to do is decide upon the use you will be putting your new binoculars to. There is no such thing as a binocular that does everything well. Think about it, if the binoculars are to be used for gazing at the moon and planets, are the same ones likely to be useful at a concert? Of course not. Binoculars are mostly designed with particular uses in mind, though there are some good 'general purpose' ones too.
Those numbers on all binoculars refer to the magnification factor and the diameter of the lenses. So an 8x 42 has 8 times magnification with a 40mm lens. The greater the magnification the poorer the image quality and the harder it is to hold the binocular steady enough to actually enjoy the view. Most people find 8-10 times magnification to be the most useful and comfortable for outdoor use. Concert viewing requires maybe a 4 times binocular.
The diameter of the lens is important too as the bigger it is the more light is captured so the better the image tends to be, it also gives you a wider area to see (or field of view). This field of view is usually expressed as an angle or as the number of feet the view from side to side appears at 1000 yards. The smaller the FOV the harder it is to spot your target.
Those are the most basic factors, after these we start to get into a few more technical aspects such as the type of glass used and eye relief. This eye relief factor is important if you like to wear your glasses while using binoculars. It refers to the distance between your eye and the binocular eyepiece. Why is that important? Because if you wear glasses while viewing you'll need to allow for the extra distance to your eye caused by your specs between the binoculars and your eyes.
The coatings used on binocular lenses and prisms adds to their quality and price. Various coatings do different things but their main job is to prevent light being lost by reflection. The sophistication of the coatings used will make quality and price vary wildly from type to type and brand to brand.
Other than those points you should also consider whether you need attributes such as waterproofing, robust construction for wear and tear and the like. Remember the more you need out of your binocular the more it is likely to cost you so when you have narrowed down to this point, get the best you can afford - you'll never regret it!