Cockpit uses the PackageKit D-Bus API to get information about available package updates and to apply them, in an Operating System independent manner.

To perform similar tasks from the command line, use the pkcon command:

$ pkcon refresh

$ pkcon get-updates
Available  sudo-1.8.20p2-1.fc26.x86_64 (updates-testing)
    Allows restricted root access for specified users
Available  vim-filesystem-2:8.0.617-1.fc26.x86_64 (updates-testing)
    VIM filesystem layout
Available  vim-minimal-2:8.0.617-1.fc26.x86_64 (updates-testing)
    A minimal version of the VIM editor

$ pkcon get-update-detail sudo
Details about the update:6.x86_64 [fedora]
 Package: sudo-1.8.20p2-1.fc26.x86_64
 Bugzilla: https://bugzilla.redhat.com/show_bug.cgi?id=1452941
 Update text: - update to 1.8.20p2
    - added sudo package to dnf/yum protected packages

$ pkcon update
The following packages have to be updated:
 sudo-1.8.20p2-1.fc26.x86_64	Allows restricted root access for specified users
 vim-filesystem-2:8.0.617-1.fc26.x86_64	VIM filesystem layout
 vim-minimal-2:8.0.617-1.fc26.x86_64	A minimal version of the VIM editor
Proceed with changes? [N/y] y
[...]

Of course you can also use your Operating System specific commands for that, such as dnf updateinfo info on Fedora or sudo apt upgrade on Debian.