What is a nuclear criticality accident?

First off, nuclear criticality refers to a fission chain reaction, such as in a nuclear power reactor. The fission of a nuclear bomb, in contrast, usually involves a level of super-criticality, because more neutrons are being produced than when the reaction was started. Power plants' reactors contain less-enriched fuel (3% concentration of fissile uranium) than a bomb (99% conc.) since they're only trying to heat up water to 550 degrees for steam-- not to burn up a city. However, when we started harnessing the atom for electricity, trying to get the concentration of fuel just right proved to be tricky. You've heard of critical mass? This is an amount of a particular form of uranium that is needed for criticality to occur. Once when some uranium fuel was being mixed up, it stopped stirring; imagine if you add sugar to iced tea, stir it, then look to see the undissolved sugar swirling in the bottom of the glass-- when the fuel stopped being stirred, the uranium fell out like sugar, gathered at the bottom, and the mixture "went critical" unexpectedly (Flash / Woof). This was a criticality accident, and workers in the immediate vicinity were real unlucky. This was a tough lesson, and they changed methods so that this accident won't be repeated. Interesting stuff-- for more nuke info, research Oak Ridge or NRC's website.