I receive a number of notifications from ESET Smart Security about Port Scanning attack. But I'm behind a router. But as far as I know, computers behind a router is not accessible from others (Please correct me if I'm wrong). Then how can ESET report about such an attack.
A router (or "Internet gateway") is almost transparent to Internet protocol packets: it only decrements the "TTL" field of packets (Time-to-live, the number of routers, and number of seconds, an IP packet can go through before dying/expiring).
To perform IP filtering, you need a firewall. Firewalls are often configured on routers, but it is a distinct function, that must be configured (mostly) inpendantely.
Almost all "NAPT devices" that is Network Address and Port Translation devices:
A NAPT device look like a router "from the inside" (the LAN ports) and must be configured as the "Internet gateway" on computers connected to the LAN Ethernet ports. But it is wrong to describe a NAPT device as a "router" because: