This is interesting and confusing for a couple reasons.
For one, we often talk about web server sessions. The server maintains some state and remembers the user and what they're doing and that sounds a lot like the definition of a connection. The distinction is that web servers build their session stuff on top of the HTTP protocol, and session is not part of the HTTP protocol. You can have HTTP servers with no sessions.
Another confusing bit is that IP is connection oriented. HTTP makes an IP connection for the duration of one HTTP request-response and then breaks it. If you read up on HTTP there is a three part handshake - three IP messages - to one request. I'm foggy on this but it's something like
Client: I'd like to send you a message
Server: Ok, send me a message
Client: Here's the message.
I think it's cool that we run connection oriented web sites over connectionless HTTP over connection-oriented IP over connectionless TCP. Protocol stacks can be fun.