The hostname part of the URL is, of course, simply a name that can be resolved to a numerical IP address, or the numerical address itself.
curl http://example.com
When specifying a numerical address, use the dotted version for IPv4 addresses:
curl http://127.0.0.1/
…and for IPv6 addresses the numerical version needs to be within square brackets:
curl http://[2a04:4e42::561]/
When a hostname is used, the conversion of the name to an IP address is
typically done using the system's resolver functions. That normally lets a
sysadmin provide local name lookups in the /etc/hosts file (or equivalent).
curl knows how to deal with IDN names and you just pass them on like you would a normal name:
curl https://räksmörgås.se