Napoli moved quickly to bring in a new coach who they thought would be able to improve their game next season, Antonio Conte was the name they finally chose to appoint as coach. Previously they were also linked with the Atalanta coach and this rumor was actually the strongest news, but it turned out that Antonio Conte was their final choice.
Napoli are well aware of the decline they have experienced this season, so they will do whatever they can to improve their game next season, including spending a lot of money to bring in a new coach. Napili hopes that Conte's joining as coach can provide fresh air for Napoli's very disappointing game this season.
This is a decision that I think Napoli took correctly, because their previous coach did not make any progress so they had to look for a new coach who was thought to be able to improve the performance of the team's game.
I do not think that they actually "moved quick"

. In a cheeky sense, they probably had Conte ready for a long time and did not really get him quickly, they probably agreed with him verbally for a month or maybe more now, and they said they will sign the contract when the season ends, and that is why it looked quick, but in reality wasn't.
I can't know for sure of course, maybe they had just one talk and everything was set, maybe that was the case, I do not really know, I just think that we are talking about way too quick, like can't be one phone call, so it must be done before it was officially declared. I think Napoli will do much better next season, top five at least, because Conte is an amazing manager who can bring the best out of any team.