Backing up your tickets and projects in Jira Cloud is very easy, but it is not really what you'd call a 'backup process'. The prescribed method to doing this (source: Atlassian) is by using the export feature which is explained below. Please note, that this method has a lot of limitations which are identified at the bottom of this page.
Log into Jira Cloud
(you must have administrator level access)
Select SETTINGS / SYSTEM
In the IMPORT AND EXPORT section, select Backup Manager
Under Backup for cloud, select Create backup for cloud
(you can tick the Include additional files option if you want to include issue attachments, user avatars and project logos in the export)
After the backup is complete, select Download backup file
(Important Note: Each time you download your backup file, you run the risk of overwriting the last one so its recommended that you first archive or rename your previous backup file prior to downloading)
This process is very simple, but is hardly a robust method. Here are some reasons why;
It's manual and is reliant on someone remembering to do it
The backups can only be run once every 48 hours therefore you cannot do daily backups which severely limits your ability to restore
The backup process requires a manual download which has the risk over overwriting the previous backups and destroying your history
Not all of your Jira site is backed up, making recovery somewhat tricky
These are just the tip of the iceberg when it comes to protecting your data in Jira. We recommend that you check out the excellent range of marketplace apps to automate your backups.