what does this speech reveal about the nature of the ghost?

I'm not sure what exact speech you mean but I assume it is from the ghost explaining what happened. The ghost is not a scary ghost but a sad and tormented spirit forced to walk the night and fast in fire during the day until his sins is accounted for. He bears no direct malice against his wife Gertrude: he would rather let God deal with her. He does want vengeance against his brother Claudius.