Design
The binoculars on the left are Porro Prism (named after Ignatz Porro) binoculars. The lenses have two prisms which act as mirrors and bend the light, making the binocular tube seem longer. These are cheaper to make and also produce a better stereoscopic image.
The binoculars on the right are Roof Prism binoculars. These cost more due to the higher glass quality and prism complexity. The light path is reflected four times and produces a more compact design.
Specification
On the right side of the photo above we can see it says '8x21'. The 8 relates to the magnification, therefore the image is magnified 8 times. The 21 relates to the size of the objective lense - the lense at the end of the binoculars. The binoculars in the first image all have their objective lenses pointing to the left of the photo. The greater the magnification means that any hand movement is also magnified, so with greater magnification there is a need for a tripod or something solid to lean on. The larger the objective lense the bigger, and heavier, the binoculars are likely to be - but a larger objective lense also allows in more light - which is good for star gazing.
You will also notice that the other specification on the image is 126M/1000M. This means that when looking at an object 1000M you will see 126M of that 1000M. Another of my pairs has a specification of 99M/1000M, so I would only see 99M of a view at 1000M, which I take to mean that the magnification is better.
Usage
The binocular tubes should be close enough together so that they provide a single circle of vision when you're looking down them. If the view is out of focus, then there is a central focusing wheel, which can be seen in the photos above.
Because our eyes can focus differently, some binoculars will have individual focusing wheels on either one or both of the tubes at the end closer to the eye. This allows you to set up the binoculars beforehand so that you can use just the central wheel when actually using them.
Another important point is the weight of the binoculars. The heavier they are, the more your hands will move, making the point you are trying to view very diffcult to focus on. It's important to keep your elbows close into your body to keep the binoculars as steady as possible.
If wearing binoculars around your neck try to keep them around the cheat area so that the don't swing around too much or become an uncomfortable pain around the neck!
Which for what now?
Astronomy
My astronomy book says that the maximum diameter of a fully dark adapted pupil is around 7mm. Therefore a pair of binoculars of 7x50 would give an optimum exit pupil, as 7x50 specification worked out as 50/7 = 7.14.
Birdwatching / Wildlife observation
My bird book says that there is no one binocular that is the best choice for birdwatching. Therefore it's important that you go for a binocular that you are happy with. It would seem that a magnification between 8x and 10x is popular; with 8x allowing a closer focusing. Remember that the larger the objective lense the brighter the image, therefore a larger objective lense between 42mm-50mm may be necessary if observing in poor light conditions, dusk for instance.
Sources
The Complete Illustrated Encyclopedia of British and European Birds. ISBN 978-1-84786-225-9.
An Introduction to Practical Astronomy. ISBN 1-85627-647-3.
