Chemistry - What really happens atomically in an explosion?
Solution 1:
The combustion of alkanes like butane is fearsomely complicated involving dozens of transient compounds and hundreds of different reaction. If you have a few spare hours there is a dissertation that presents a nice summary of the process here (this is a 1MB PDF).
A butane molecule is pretty stable and doesn't react with oxygen on contact so you need some way to get the reaction going. Typically the reaction is started by the generation of free radicals. These will react with stable molecules to split them up and generate more free radicals so in effect we have a chain reaction.
So the ignition process is basically the generation of free radicals, and that's what the lit cigarette does. The heat of the burning tobacco generates free radicals that then start the butane oxygen reaction. You can also generate free radicals in lots of other ways e.g. using shock, from an electric spark, or by using a suitable catalyst such as the catalytic convertor on your car exhaust.
Solution 2:
The butane and oxygen in the room are in a metastable state. An example energy diagram of a metastable state is shown in the image below. Before throwing in the cigarette, the butane and oxygen molecules are in the state labeled as 1. This state is metastable because there is a lower energy state (which makes it statistically more probable) available if they were to combine to form $CO_2$ and $H_2O$. This lower energy state is represented by the 3 in the image.
The problem is that there is an energy barrier which must be overcome for them to get to this more stable state. This is where the cigarette comes in; it adds some thermal energy which pushes the system over the energy barrier (state 2 in the image) and allows it to fall into its more stable state. In the process the excess energy gained from moving from state 1 to state 3 is given off as heat. This excess heat causes more molecules in the area to combine, and you end up with a runaway reaction known as an explosion.
*Image taken from the Wikimedia Commons.
Solution 3:
The butane and oxygen molecules' electrons gain enough kinetic energy to overcome the potential barrier that prevented them from disassociating from their respective molecules making the hydrogen and carbon atoms bond with oxygen – producing $\ce{CO2}$ and $\ce{H2O}$ and extra heat. Which would go to increase more electron's kinetic energy as well as increase the pressure of the air (since that what happens when gasses heat). This sudden increase in pressure is an explosion.