Why is the auto ignition temperature of petrol higher than that of diesel?
Auto ignition temperature is defined like this by Wikipedia:


  The autoignition temperature or kindling point of a substance is the lowest temperature at which it spontaneously ignites in normal atmosphere without an external source of ignition, such as a flame or spark. This temperature is required to supply the activation energy needed for combustion.


Gasoline (or petrol for non-americans) has an auto-ignition temperature about 50 °C higher than diesel. 

The answer boils down to explaining why the typical chemicals making up the two fuels have different activation energy barriers to combustion in air. This reaction basically involves the constituent molecules getting enough energy to react with oxygen.

We can get a crude (and probably oversimplistic) understanding by looking at the typical components of the two fuels. Diesel tends to be made up from linear saturated hydrocarbons; petrol is typically a mixture of branched and unsaturated hydrocarbons. So, a little simplistically, the typical component if diesel will have a larger surface area than a typical component of petrol (branched chain hydrocarbons are more "bunched up" than their linear counterparts with the same number of carbons). To put it another way, in linear hydrocarbons each carbon is has, at least, two hydrogens between it and any surrounding oxygen molecules from the air but in unsaturated or branched hydrocarbons the component carbon atoms are often buried inside because they are surrounded by other carbons (consider the molecule shapes of linear hexane and 2,2 dimethyl butane which have the same number of carbons). 

This is a very simplistic way of looking at the question but give a little insight. In typical diesel compound there are simply more opportunities for oxygen to attack the molecule and kick off a reaction because the amount of the molecule exposed to the outside is higher. By being more compact (lots of carbons buried deep inside the molecule) there is less opportunity for this in the components of petrol.

For the reaction to kick off some of the molecules in the mix have to have enough thermal energy to react when they meet. And oxygen has to hit the hydrocarbon hard enough or there is no reaction. Once an oxidation reaction starts, it releases energy increasing the likelihood of another molecular reaction. At a certain point when there is enough energy from new reactions and the mix doesn't spread this out too quickly, this becomes a runaway process and the mixture goes bang. This process is–at the molecular level–easier for diesel than petrol because the chances of an oxygen causing a chemical changes when hitting a hydrocarbon is higher.

Of course a lot of other factors are involved but this crude picture gives at least some useful insight. This was discovered experimentally in the early days of engine design as the designers observed that different extracts from oil had different combustion properties in engines and refined the way oil was distilled to give them the behaviours they wanted in their engines.