They burst into flames (some of them do, sodium and lithium don't) because:
1. The reaction with water produces hydrogen which can burn.
2. The energy released by the reaction is released very quickly, which ignites the hydrogen.
The energy release is quick because alkali metals' enthalpy of ionization is lower than any other metals'. This means very little energy is needed for a group 1 metal to lose one electron, so they ionize faster than other metals can, which means the overall reaction if fast, which means the energy is released in a quick burst, which results in a higher temperature - enough to ignite hydrogen - than if it were released more slowly.
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