Each HTTP request can be made authenticated. If a server or a proxy want the user to provide proof that they have the correct credentials to access a URL or perform an action, it can send an HTTP response code that informs the client that it needs to provide a correct HTTP authentication header in the request to be allowed.
A server that requires authentication sends back a 401 response code and an associated WWW-Authenticate: header that lists all the authentication methods that the server supports.
An HTTP proxy that requires authentication sends back a 407 response code and an associated Proxy-Authenticate: header that lists all the authentication methods that the proxy supports.
It might be worth to note that most websites of today do not require HTTP authentication for login etc, but they instead ask users to login on webpages and then the browser issues a POST with the user and password etc, and then subsequently maintain cookies for the session.
To tell curl to do an authenticated HTTP request, you use the -u, --user option to provide username and password (separated with a colon). Like this:
curl --user daniel:secret http://example.com/
This makes curl use the default Basic HTTP authentication method. Yes, it is actually called Basic and it is truly basic. To explicitly ask for the basic method, use --basic.
The Basic authentication method sends the username and password in clear text over the network (base64 encoded) and should be avoided for HTTP transport.
When asking to do an HTTP transfer using a single (specified or implied), authentication method, curl inserts the authentication header already in the first request on the wire.
If you would rather have curl first test if the authentication is really required, you can ask curl to figure that out and then automatically use the most safe method it knows about with --anyauth. This makes curl try the request unauthenticated, and then switch over to authentication if necessary: