(I'll use the UK spelling with an "s.") "Realisation" can have two different meanings. This is the less common meaning.
Usually, "realisation" means something that happens in our minds. We see things in a new way, or we become aware of something.
"I wondered why there was no mail, then suddenly realised it was Sunday."
"Realisation" can also mean something happening in the real world. It can mean that a possibility becomes real. It can mean that
--something imagined has been built,
--something has been achieved,
--something unlikely has happened.
In your passage, Vesuvius was always a risk, and when it erupted, that risk was realized, in a "vivid and violent" way.
Here are some other examples of this usage:
"Walt Disney World is the full realisation of Walt Disney's dream."
"In 2002, a computer model showed that the effect of a hurricane on New Orleans would be disastrous. During Hurricane Katrina, the worst fears of the engineers were realised."