Pressure, as abhijeet says, is a force applied on a certain area. Thats still somewhat bookish eh! All right....lets take an example of air pressure. Air pressure is the result of cramming air into a certain space. Cram air inside somewhere i.e. more air than is usually 'normally' present around us (thats air at 'atmospheric pressure) and it tries to escape, meaning it exerts a 'force' on the walls of the container in an attempt to escape from it. The more air you cram in, the higher is this 'force' or 'pressure' that it exerts in trying to escape into the atmosphere. To increase your bike's 'tyre pressure' for example, you fill it with more air. More air into the same amount of space (or volume as three-dimensional space is called) pushes harder from the inside of the tyre and at the inside of the rim i.e. it tries to escape with more 'force i.e it exerts more force per unit area on the inside of the tyre. And in resisting this 'attempt' of air to escape, the tyre becomes stiff. Allow this air to escape through a puncture (i.e. reduce the amount of air inside the tyre) and the pressure 'drops' inside the it and the tyre goes limp. As a proof of this need for 'more' air to increase pressure, try inflating your bike tyre and an SUV's tyre with a foot pump. While the bike tyre will inflate to say 25 psi with some 50-60 strokes of the pump, you'll need to pump away for some 4-500 odd strokes to get the same 'pressure' reading for the SUV tyre.
The same 'physical' understanding can be extended to any 'pressure'. The piston travels from the Bottom Dead Center (BDC) to the Top Dead Center (TDC) during the compression stroke. In doing this it effectively reduces the volume available to the air inside the cylinder. Reduce volume or increase the quantity of air in the same volume...the effect is the same....which is to increase 'pressure'. So we say that the air has been compressed. When fuel gets burnt in this compressed air, the rise in temperature further increases the pressure and so forces the piston downwards, making it rotate the crank and you get the power stroke.
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