HTTP 202 Accepted (HTTP/1.1)
You are looking for HTTP 202 Accepted status. See RFC 2616:
The request has been accepted for processing, but the processing has not been completed.
HTTP 102 Processing (WebDAV)
RFC 2518 suggests using HTTP 102 Processing:
The 102 (Processing) status code is an interim response used to inform the client that the server has accepted the complete request, but has not yet completed it.
but it has a caveat:
The server MUST send a final response after the request has been completed.
I'm not sure how to interpret the last sentence. Should the server avoid sending anything during the processing, and respond only after the completion? Or it only forces to end the response only when the processing terminates? This could be useful if you want to report progress. Send HTTP 2102 and flush response byte by byte (or line by line).
For instance, for a long but linear process, you can send one hundred dots, flushing after each character. If the client side (such as a JavaScript application) knows that it should expect exactly 100 characters, it can match it with a progress bar to show to the user.
Another example concerns a process which consists of several non-linear steps. After each step, you can flush a log message which would eventually be displayed to the user, so that the end user could know how the process is going.
Issues with progressive flushing
Note that while this technique has its merits, I wouldn't recommend it. One of the reasons is that it forces the connection to remain open, which could hurt in terms of service availability and doesn't scale well.
A better approach is to respond with HTTP 202 Accepted and either let the user to get back to you later to determine whether the processing ended, or notify the user when the processing is done if you're able to call the client back for instance through a message queue service (example) or WebSockets.