More concretely, they can run the equivalent of `ip route add 192.168.1.0/24 via <your WAN IP>` on a machine that's connected to your WAN network, and then their machine will send packets with a dest of 192.168.1.x to your router. Your router will route them onto your LAN because that's what its own routing table says to do with them.
Anyone on your immediate upstream network can do this, not just your ISP. Also, if you use ISP-assigned GUAs then this inbound route will already exist and anyone on the Internet can connect. Applying NAT to your outbound connections will change their apparent source address, but it won't make that inbound route disappear.