Ok, it's quite a fussy screen, but we can break it up. It is not the JIRA (JIRA core) default screen, let's forget that for now.
The left hand side is the view of a "scrum board". Lots of "cards" in columns showing you progress. Each "card" is a JIRA issue.
The right hand side is the "detail view" of the last issue you clicked on in the board view. It's trying to show you issue details.
This view is configured on the board, not by plain JIRA Core. If your screen were wide enough, you would see a link to board configuration on the right hand side of the header (further over than "recently updated") and the board configuration is where you can choose fields for the detailed issue view.
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