Simply put it's a fancy wrapper around podman, docker or lilipod to create and start containers highly integrated with the hosts.

The distrobox environment is based on an OCI image. This image is used to create a container that seamlessly integrates with the rest of the operating system by providing access to the user's home directory, the Wayland and X11 sockets, networking, removable devices (like USB sticks), systemd journal, SSH agent, D-Bus, ulimits, /dev and the udev database, etc...

It implements the same concepts introduced by https://github.com/containers/toolbox but in a simplified way using POSIX sh and aiming at broader compatibility.

All the props go to them as they had the great idea to implement this stuff.

It is divided into 12 commands:

distrobox-assemble - creates and destroy containers based on a config file
distrobox-create - creates the container
distrobox-enter - to enter the container
distrobox-ephemeral - create a temporal container, destroy it when exiting the shell
distrobox-list - to list containers created with distrobox
distrobox-rm - to delete a container created with distrobox
distrobox-stop - to stop a running container created with distrobox
distrobox-upgrade - to upgrade one or more running containers created with distrobox at once
distrobox-generate-entry - to create an entry of a created container in the applications list
distrobox-init - the entrypoint of the container (not meant to be used manually)
distrobox-export - it is meant to be used inside the container, useful to export apps and services from the container to the host
distrobox-host-exec - to run commands/programs from the host, while inside of the container

above quoted from here: https://github.com/89luca89/distrobox/blob/main/docs/README.md#what-it-does