Oh I see now, so the combustion happens in the cylinders then? That explains why they all work in sequence and why you need pairs, because they provide opposite sides of the rotation for the main shaft!
It gets comlicated as there are probably exceptions to the norm in every area of an engine. For this explanation, the 'stroke' of an engine is the distance the piston travels down (or up) in the cylinder. Nearly all car engines are 4 stroke, meaning the each piston (inside the cylinder) will need to complete 4 strokes to complete one combusions cycle - in one revolution the piston goes down and up but for each combusion cycle the piston goes down, up, down, up. The correct terminology for the stroke is Intake (piston down), Compression (up), Combustion (down) and Exhaust (up) though it will forever be to me: suck, squash, bang, blow.
I assume by "work in sequence and need pairs" you are talking about the combustion cycle and the fact 2 pistons are up and 2 are down in a 4 cylinder engine? Ideally you want as many combustions per revolution of the engine (1 engine revolution is the crank turning 360 degrees). As the engine requires 4 strokes per combusion cycle and 1 stroke is only half a revolution, a 4 stroke engine requires 2 revolutions to complete a full cycle. To improve smoothness, power deliver, effeciency etc. the 4 pistons are doing a different step of the combusions cycle at any one time, i.e. the two pistons that are 'up' one will be on the compression stroke, the other on the exhaust. The two that are 'down' one will be on the intake stroke, the other on the combustion stroke. Due to this a 4 cyclinder 4 stroke engine will have a combustion every half a revolution. The other advantage of two up, two down is also balance, the same weight is going up as going down so it is naturaly counter balanced.
EditP On a side note, a 4 cylinder 4 stroke engine with the cylinders numbered 1, 2, 3, 4 in order will generally (but not always) fire (combustion) in the order: 1, 3, 4, 2. So each cylinder for a cycle goes
Cylinder - Stoke 1 - Stroke 2 - Stroke 3 - Stroke 4
1 - Combusions - Exhaust - Intake - Compression
2 - Exhaust - Intake - Compressions - Combustion
3 - Compression - Combustion - Exhaust - Intake
4 - Intake - Compressions - Combustion - Exhaust