Binoculars vary in optical quality and mechanical quality -- how well-made the lenses are, how well the binoculars are put together and how smoothly they focus. Binoculars are often described with two numbers with an "x" in between, such as "12 x 50" or "10 x 50."
What Are Binoculars?
A pair of binoculars is really two small telescopes connected to each other. In addition to the lenses and the frame connecting them, they have a focusing ring. Better binoculars will have a focusing ring for each eye. The lenses are coated to reduce glare and good binoculars are carefully aligned.
Magnification Power
The first number in the description of binoculars refers to magnification power. "12x" means that they will bring images 12 times closer than they would be with the naked eye. At first, it might seem that higher numbers are better, but this is not necessarily the case, because the higher the magnification, the harder it is to hold an image steadily in your view. It is therefore a tradeoff: Higher magnification is better if you will be stationary and are able to brace your hands or arms on a steady surface; they are also better if you will have to see small objects at a great distance. But lower magnification is better if you will need to focus quickly or while moving. Both "10x" and "12x" are on the high end of magnification and may be hard to hold steady enough to see.
Objective Lens
The second number is a measurement of the size of the front lens in millimeters. "10x50" and "12x50" lenses are both 50 millimeters in diameter -- a little less than 2 inches. Larger lenses let in more light, which lets you see in darker situations. But they also make the binoculars larger and heavier. So it is again a tradeoff. Larger lenses are better if you will often be in low light and -- as with higher power -- if you will be able to brace your arms against something. Smaller lenses are better if you will be carrying a lot of other things or will need to hold the binoculars steady without bracing your arms.
More Advice
Beyond these two numbers, binoculars vary greatly in quality, as do cameras or telescopes or other optical equipment. If you are going to be using the binoculars a lot, it is worth doing more research and buying from a store that has expert salespeople. On the other hand, if you will only use your binoculars a couple times a year, then it may not matter too much to you.