To the right of the search box on the web app's record editor, you will see a button with three red lines. This button will open the column setup window.
In this window, you can enable and disable the fields that you wish to have displayed in the table. You can also click and drag on the three horizontal lines to move the ordering of the columns in the table.
When you run an export using the Download Data button on the record editor, the exported data file will only contain the columns that are visible in the data table. However, there are a few columns that are deemed to be critical, the record ID columns, the geometry, and the Latitude and Longitude columns. Since these are necessary columns for the importer, they are always included in the export data file.