You specify the resource to download by giving curl a URL. curl defaults to downloading a URL unless told otherwise, and the URL identifies what to download. In this example the URL to download is http://example.com:
curl http://example.com
The URL is broken down into its individual components (as explained elsewhere), the correct server is contacted and is then asked to deliver the specific resource—often a file. The server then delivers the data, or it refuses or perhaps the client asked for the wrong data and then that data is delivered.
A request for a resource is protocol-specific so an FTP:// URL works differently than an HTTP:// URL or an SFTP:// URL.
A URL without a path part, that is a URL that has a host name part only (like the http://example.com example above) will get a slash ('/') appended to it internally and then that is the resource curl will ask for from the server.
If you specify multiple URLs on the command line, curl will download each URL one by one. It will not start the second transfer until the first one is complete, etc.