FIREWALL: TCP State Check and Replay Check

Hi,
in my router's log messages I find:

Nov 29 20:42:11 FIREWALL exact tcp state check (1 of 11): Protocol:
TCP Src ip: x.x.x.x Src port: y Dst ip: myIP-WAN Dst port: z

Nov 29 20:42:05 FIREWALL replay check (1 of 15): Protocol: TCP Src ip:
myIP-LAN Src port: y Dst ip: z Dst port: x

I recognize the two connections and they're both authorized.

By the way, I'm asking:
- What is 'exact tcp state' and what does it? Is that necessary?
- What is 'replay check'? and what does it? Is that necessary?

Thank you