Boyle's Law simply describes the relationship between the pressure and volume of an enclosed gas when Temperature remains constant. That relationship, usually expressed as P_{1}V_{1} = P_{2}V_{2}, just means that the product of pressure x volume remains unchanged as either or both are changed.
Since pressure x volume remains constant, for example, doubling the pressure on an enclosed gas will reduce its volume to 1/2 its previous size. Tripling the pressure will reduce its volume to 1/3, and so on. Alternatively, if you double the volume available to an enclosed gas, pressure is halved.
The simplest demonstration of Boyle's Law is a hand bicycle pump. By pushing down on the
piston, the reduced volume increases the pressure of the air inside so that it is forced
into the tire. Because pressure changes will have an affect on temperature (feel the pump after a few seconds of pumping), temperature must be allowed to return to its prior value
for Boyle's Law to hold true.
Answered by:
Paul Walorski, B.A., Part-time Physics/Astronomy Instructor

Boyle's Law is a statement of the relationship between the pressure and volume of gasses. Specifically it states that under isothermic conditions, the product of the pressure and volume remains constant, or
P_{1} x V_{1} = P_{2} x V_{2}
where P_{1} is the pressure before some change, V_{1} is the volume before the change, P_{2} and V_{2} are the new values after the change. Another way of thinking about this law is that the values of pressure and volume are inversely proportional; if one goes up, the other must decrease by the same factor. If you trap gas in a cylinder, and then reduce the internal volume of the cylinder to half its original value, the pressure will double.
Why does this happen? If you squeeze those gas molecules from the above example into half the volume, you would expect them to be packed closer together and to slam into the sides of the container more often. The sum of all those little collisions is what we call pressure.
Answered by:
Rob Landolfi, Science Teacher, Washington, DC

'A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data. God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe.'