Binoculars

From KayakWiki

Binoculars are small pairs of telescopes that allow the user to observe distant objects with both eyes.

Compact binoculars are perfect. Larger binoculars are preferred only if you have other needs for binoculars, such as birding or wildlife observation, astronomy etc. Waterproof binoculars are not essential, but highly recommended. A strap that will provide flotation is a good idea, too. You can get expensive, high-quality optics or lower cost, decent quality optics depending on your preferences and bank balance.

Binocular specifications
The most common specification used for binoculars identifies the magnification and objective lens diameter in the form MxOS, where M is the magnification and OS is the objective lens diameter in millimeters. For example, a pair of binoculars with a 24mm diameter objective lens and 8 times magnification will be specified as 8x24 binoculars.
Magnification
Magnification should be no more than 8 times unless you purchase image-stabilized binoculars. More than 8 power binoculars are very difficult to hold steady on the water; many paddlers would prefer 7 power.
Objective lens
The objective lens is the lens closest to the object you are observing. Objective lens sizes of around 21-25mm are adequate for most navigation purposes. The larger the objective lens, the greater the amount of light that the binoculars will collect. Large objective lenses means that you will see brighter images late in the day and see more in the night sky. However, increasing the size of the objective lens will increase the size and weight of the binoculars.
Exit pupil
The light leaves the eyepiece in a small circle known as the exit pupil. The exit pupil size is equal to the objective lens size divided by the magnification. For example, 8x24 binoculars have an exit pupil size of 24/8 = 3mm. An exit pupil larger than about 7mm will be larger than the entrance pupil of your eye under dark conditions and any light in the area outside your eye's pupil will be unused. For that reason, overly large exit pupils are not useful. Too small an exit pupil will be hard to find - it will be like looking for a pinhole at the back of the binoculars. Sizes between 2.5mm and 5mm are the best range for most uses.
Prism type
There are several arrangements of prisms that can be used in binoculars. The prisms are used to reduce the overall length of the binoculars while providing a long optical length. This is not a very important factor for most uses. The two most common types are roof prisms and porro prisms. Roof prisms provide for a more compact binocular but will be slightly poorer in performance in lower cost binoculars. In high priced binoculars, roof prisms are as good as porro prisms and porro prism designs are becoming less common.
Materials used
There are many materials used in making binoculars. Most of these do not factor into your purchase decision unless you are buying one of the better quality binoculars and are looking for binoculars with specific uses in mind. The materials of particular interest are the glass types (with properties such as dispersion, refractive index and so on being important), body type, which will affect weight and strength and whether or not the binoculars are sealed and filled with inert gas, which would prevent fogging.
Glass coatings
Cheap binoculars will have uncoated optics, while better quality binoculars will have some or all glass surfaces coated. The difference will be how much light is able to get through the lens system versus how much is reflected. High transmission will mean better low-light performance and less internal reflection. The latter will cause a loss of contrast in the image and will reduce image quality.
Eyeglass wearers
If you wear glasses, you will want binoculars with high eye relief – look for 11mm or more. Eye relief indicates the distance the binoculars can be held from the eye while still observing a full field of view.
Manufacturers and retailers
There are many good brands of binoculars, including Leica, Minolta, Nikon, Pentax, Steiner, Swarovski, Zeiss, Bushnell and Celestron. Camera, astronomy and birding stores are better sources for binoculars and binocular information than department or hardware stores.
Monocular
A small telescope, looking like half a pair of binoculars, is often called a monocular. Many kayakers prefer a compact monocular for navigation. These will be half the size and weight of equivalent binoculars.

References:
For more details, see the Wikipedia binocular entry.