In your case, using an old host with PHP 5.6, you should make a backup using setup (upper login) and click on [Database backup], then [Backup now] and download the backup.
Then you need to make a new installation of EGroupware 19.1 following the instructions in the wiki on Github: https://github.com/EGroupware/egroupware/wiki/19.1--Installation-using-egroupware-docker-RPM-DEB-package
Once you have a new empty EGroupware installation, you need to do the following steps:
- rsync the files directory (by default /var/lib/egroupware/default/files) to the new installation
- login to setup (upper login) restore the backup you made from 1.6 and click on update
You can skip step 1. but that means loosing all files and attachments.
I you want to have a quick test of the update, create a trial in our hosting (https://www.egroupware.org/trial), login with your sysop credentials, go to Admin >> Database backup and restore and restore your 1.6 backup.
Docker is a technology to run Linux container on a host. Docker is the default way of installation for EGroupware 19.1 either through Linux packages (containing docker-compose files) or docker-compose directly.