Router Log: "Remote access to LAN", newtork slowdown?

My internet connection was slow, so I looked at the router configuration software to see the router statitistics and status. The Log had a long list of IP addresses that had the message remote access to Lan IP 192.******:5****. The Lan IP is the computer of a wired client on my network. I have the remote access check box unchecked in the configuration file; however the everyone box is checked. What does this remote access in the log mean? Is it bit torrent, file sharing, instant messaging, gameing software? Is this a security concern for the network? Is this the likely cause of the network slowing down?

I want to minimize network restrictions, but I also do not want network slowdowns or security risks.