The folks over at uBreakiFix decided to put together a little video that purports to explain why lithium batteries explode. They do briefly, only very briefly, mention that abnormalities in the flow of ions between the positive and negative electrodes is what can trigger an explosion. They also suggest that one potential cause of an abnormality would be overcharging. Unfortunately, that is the extent of the attempt to explain why lithium batteries explode although they do try to make up for it with several clips of exploding batteries.
The video explains the team decided to test batteries to see what it takes to make them explode. To accomplish this the uBreakiFix team took a bunch of batteries, removed the safeguards, and then pumped them full of too much voltage. The results are quite spectacular.
The uBreakiFix team also has some suggestions to help ensure a long, safe life for your lithium batteries and the devices containing them. This includes things like not letting the batteries overheat and using the correct charger. They also mention the more common problem of batteries swelling due to the gases trapped in the case, a situation that calls for replacing the battery.
You can check out the video below of all the explosive action even if it does not really help explain why a battery in normal conditions might end up exploding.