ssh-copy-id is a script that uses ssh to log into a remote machine (presumably using a login password, so password authentication should be enabled, unless you’ve done some clever use of multiple identities)

It also changes the permissions of the remote user’s home, ~/.ssh, and ~/.ssh/authorized_keys to remove group writability (which would otherwise prevent you from logging in, if the remote sshd has StrictModes set in its configuration).

If the -i option is given then the identity file (defaults to ~/.ssh/identity.pub) is used, regardless of whether there are any keys in your ssh-agent. Otherwise, if this:

ssh-add -L

provides any output, it uses that in preference to the identity file.

If the -i option is used, or the ssh-add produced no output, then it uses the contents of the identity file. Once it has one or more fingerprints (by whatever means) it uses ssh to append them to ~/.ssh/authorized_keys on the remote machine (creating the file, and directory, if necessary)