One of the computers on your home network will often be assigned 192.168.1.101 automatically via a router's DHCP configuration. The DHCP range on many Linksys routers starts one number earlier, at 192.168.1.100 by default. The first computer you connect to the router will receive this address, and the second one will receive 192.168.1.101 subsequently.
192.168.1.101 is a private (non-routable) IP address. Therefore, you will not find any hosts on the public Internet with this address. If you see messages from your network router pertaining to 192.168.1.101, you can expect those are originating from one of your own local computers.