At the TCP level, the only addressing that you can see is the IP address and TCP port number of each end of the connection. TCPLogView is doing exactly what it is designed to do. Other protocols ride inside a TCP connection to provide services like web browsing (HTTP), file transfer (FTP), and mail transfer (SMTP). If you wish to capture what the various protocols that ride inside TCP datagrams are doing, you'll need a program that understands how to interpret that particular protocol.
There are also other transport layer protocols, like UDP, which can be used to send data over the network. If you want to know the full network activity of an application, you'll need to consider more than just TCP activity. Without knowing more about what you want to accomplish, it is hard to suggest an appropriate tool.
For HTTP, which I'm guessing is what you want based on the question, Wireshark and Fiddler are pretty good. Wireshark is the more general of the two tools.