There are many explanations of how points and coils work online. It is difficult to explain without knowing your current level of understanding.
Simply put the points are simply switches timed to the rotation of the crankshaft.
When the points are closed power flows from the battery to the primary side of the coils, creating an EM field in the coils.
When the F timing mark is reached the points open causing the primary side of the coil to quickly change to zero volts. As this occurs the EM field collapses and induces a voltage in the secondary side of the coils (the coils are electrical transformers which conduct in response to a changing EM field such as the one collapsing in the primary wires)
As the field in the secondary builds it reaches a point that the gap of the plug develops sufficient potential to cause a spark to discharge the coil.
This charge through the points/discharge through the plug cycle is repeated each time the crank shaft goes through one revolution.
Honda fours use a dual wound coil that fires two pugs simultaneously, one in a cylinder just before Top Dead Center on the compression stroke, one in a cylinder TDC on the exhaust stroke. This was done to allow two points to run a four cylinder motor with out a distributor system as seen a car engine where they have more room.
The condensers suppress the voltage bounce on the primary wires when the EM field is collapsing, this reduces sparking across the point gap which damages the mating surfaces.
Optimizing the Standard SOHC4 Ignition System
http://www.motorcycleproject.com/motorcycle/text/sohcign.html
