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State table will be kept for stateful (TCP) and stateless (UDP, ICMP) protocols. If you untick "Enable Firewall" as well, then state table will not be kept for that IP and all inbound packets will be sent directly to your TCP/IP stack (or to a software firewall of your choice).
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Your PC/NIC will then get an external (WAN) IP assigned to you by your ISP and no LAN is available. If you untick "Enable NAT" then your router will run in "bridged" mode. Some may find this type of check insufficient so there is an option to untick the "Firewall" option in a router and use a software firewall of your choice.
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It is a simple IP/port check mechanism which will ensure that only requested inbound packets are forwarded to your IP (based on what has been requested by outbound). In most, if not all home routers the term "firewall" will refer to a state table.
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