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Too much information can lead to chaos. Too little information can lead to ambiguity and lack of control. Ability to customize a list of columns accessible from Plan View is a step towards adjusting the view dependent on needs and purpose which leads to accessing data that matters in specific context, your context. 

To edit what columns are displayed on Boards' Plan View, you have to customize the Precursive Tasks Field Set called Plan View Columns (taskfeed1_Tasks_Header_in_the_Plan_View). That is accessible from the Precursive Task object. Please see this article for Customizing Precursive Page Layouts and Field Sets to learn more.

Here's what you need to know first:
 

What to Know when Customizing Boards Plan View

• It is not possible to display field types that can handle multiple lines of text or data (i.e. Multi-Select Picklist, Text Area default/Long/Rich, Text encrypted)
• You can display up to ten columns/fields that meet previous criteria
• Tasks' Name is always displayed even if removed from the 'Plan View Columns' Field Set
• Export the Plan into an Excel file, Start and End Date fields need to be added to the Field Set.

Related Resources

Customizing Precursive Page Layouts and Field Sets 
Export the Plan