The term next-generation firewall is not well defined, so it’s worth clarifying a little before we proceed.
Put simply, a next-generation firewall offers more protection than a traditional firewall as it can look inside content, rather than just blocking based on sources and destination.
A useful analogy is the postal service. A traditional firewall just looks at the address on the envelope and uses simple rules to decide what’s permitted.
A next-gen firewall can look inside the envelope to check it also doesn’t contain dangerous content. Likewise, it can have smarter rules so you can say “block all known dodgy addresses” rather than having to explicitly state “don’t allow mail from Joe the scammer at number 23 Spam Lane.” SRC
The great thing about these smart rules is that you can transfer the responsibility for keeping an updated list of dodgy addresses to your firewall vendor rather than maintaining them manually yourself.