In my router I have this option:
I know what is NAT, but what does it mean the bridge option here? and how the NAT is related to it? what is more secured
Missing information: device brand and model. My best guess at the moment:
Enable: device act as a router, external/WAN/ISP interface is connected to one subnet and internal/LAN interface to another. Outbound traffic from LAN to WAN is NATed behind external IP address.
Disable: device act as a router, external/WAN/ISP interface is connected to one subnet and internal/LAN interface to another. Outboud traffic from LAN to WAN is forwarded with original source IP address.
Bridge: device act as bridge/switch, and both external/WAN/ISP interface and internal/LAN interface(s) are on the same network (broadcast domain).
Bridge, I assume, is used for IPX/SPX over TCP/IP and what not. Network Address Translation is for using an internal network with one of the set-aside private blocks like 192.168.x.x, as opposed to classical routing which is a can of worms we will not get into.
Just use NAT.
It depends on your modem/ISP, which you haven't told us.