As many others have explained, the karat is a unit of measurement that evaluated how much of an object is made of pure gold. The karat evaluates the object in 24 fractions and identifies them in a binary manner: gold, or not gold. Therefore 24 karat is 24/24, or 100% gold. All lesser values indicate the object is not pure gold, but it tells you nothing about what those other materials are, except that they aren't gold. 

So, 14 karat indicates 14/24 parts gold, or about 58%.

The more formal way of evaluating this is 24 x (pure gold mass / total mass). 

The word karat (or carat) is thought to have derived from the name of a seed, the mass of which may have provided an early means of measuring and comparing the values of small valuable objects. The karat system is not considered metric and generally overlaps or competes with other methods of measuring fineness, or purity, of a given object.

The purity of gold is measured in Karats, with 24 Karat representing 100% purity. The karats are defined as

K = 24 (Mp/Mt)

where, Mp is the mass of pure metal and Mt is the mass of total alloy.

Hence 24 Karat gold will have 24 parts of pure metal and 0 parts of other metals, making up the alloy.

14 Karat gold will refer to 14 parts of pure gold and remaining 10 parts (=24 parts-14 parts) other metals. In other words, 14 karat gold is 

(14/24) x 100 % = 58.3% pure.

In comparison, 24 karat gold is 100% pure.

Note that 100% pure gold is very soft and as such can not be used in jewelry and other applications. Addition of other metals provide these properties and as such, people buy 22 karat or 20 karat or 18 karat jewelry.

Gold is never 100% pure gold.  The karat, then, is a measure of how much of it is truly gold, by weight.

This is measured in parts of 24.  A 16-karat gold ring refers to the fact that 16/24 parts are actually gold.  That leaves 8/24 that is not gold, but other metals.

A 24-karat ring would be almost 100% pure gold.  It is close enough to 100% that the difference is too small to detect.

While it seems desirable to have more gold in jewelry and less other metals, it is important to know that gold is very soft and can be damaged easily. Adding in a little of those other metals gives the gold strength and makes it less prone to being scratched, bent or otherwise damaged.