Things and CheapSlider explain everything very well already.
I work a lot with distribution transformers and deal with cable faults.
As already said, previously overloading may have degraded the insulation to an extend that when temperatures changes occur cooling down or heating up the windings may make good contact and start arcing, this will create heat, expansion and bang. The mineral insulating and cooling oil will burn very well when heated.
That is the worst case scenario, normally a HT drop out fuse should operate before a transformer explodes, these go off with a bang like a shotgun and cause the sky to light up.
Although from my experience most TX's are fused with oversized fuses so protection doesn't always exist.
Sometimes deteriation of the oil may cause the problem, after years of service (30 Y + ) the oil tend to become acid and may cause low insulation resistance in the TX with increased leakage currents.
At substation TX's every half year oil samples are taken and are analysed in a lab for signs of carbon, ecythelene etc and so potential faults can be looked at well before something goes wrong. Ok these are 10 or 20 MVA and cost millions of dollars, for smaller dist TX's it is not worth doing.
We do load surveys and data readings in areas when complaints exist, These are usually pre warnings when overloading exist on the system or for pending cable faults or connection faillures.
Transformers are supposed to be designed to vent off the excess via a breather or explosion valve to a safe area.
This is not always possible on pole transformers.
I will take a few pics in the next week and provide the URL links for anyone interested.
Nigel, In New Zealand we mostly use the British system with 6.6 , 11 and 22 kV distribution voltages.
A lot of TX's are overhead 30 and 50 kVA rural, while in the city most are pad mounted TX's 100 to 300 kVA fed from OH or UG supplies and 500 kVA - 1 MVA near high load centres.
Some 325 kVA OH TX's are still in service, one only about 1 km away from my place which iw ill take a picci off.
Ok my $0.02 worth