Auto ignition temperature is the temperature at which a fuel combusts without any external ignition such as spark. This is the property with which Diesel engines (Compression Ignition) works.
The main difference between a compression ignition (Diesel) and Spark ignition (Petrol) engines is the way the fuel is injected and ignited. This difference can be understood more conveniently by taking Auto-ignition temperature into account.
Auto-ignition temperature refers to the temperature at which a fuel gets ignited without any external source like spark or flame. Different fuels have different auto ignition temperatures and it basically depends on the chemical properties of the fuel. One interesting thing to note here is that the fuel gets ignited only if it is in its gaseous state.
Now coming to the compression ignition (Diesel engines) here, the fuel is first pumped from the tank, and atomized in common rail (if it is CRDi) which is nothing but pressurising it to several hundred bars. Then injected into the combustion chamber through injectors since it is atomized before entering, it will not be a continuum i.e. it will be split into very small particles and vaporises eventually (Also taking into account of the high pressures in the chamber due to high compression ratios in CI engines). Then due to the adequate temperatures in the chamber, the fuel auto ignites.
Source: Wikipedia
This can be explained chemically. During auto ignition, this is associated with breaking of bonds of the fuel which releases lots of energy. Never confuse this with flash and fire points as it deals with vapour pressure.
This explains why diesel engines operates at a higher compression ratio (~16-20). Higher compression ratio not just increases the volumetric efficiency of the vehicle but also plays an important role in vaporising the fuel which would not be possible if operated at a lower compression ratio hence no auto ignition of the fuel leading to incomplete combustion. Also, cold starting in diesel engines is difficult which is why they are provided with glow plugs which is essentially an electric heater which increases the temperature of the combustion chamber.
Now question arises why petrol engines are spark ignited as it is more volatile. Volatility is not the only factor that accounts for auto ignition. As previously stated, it depends on the chemical properties of the fuel which makes it less feasible. The given data clearly proves that petrol have a higher auto ignition temperature (247 oC VS 210 oC) which is difficult to attain. Hence it operates at a lower compression ratio.