Data exported to MS Excel contain HTML tags.
MS Excel cannot properly render HTML inside cells. It can render simple formatting like bold text and colors, but it cannot render paragraphs, pictures, tables, links, and rich formatting in general in a single cell. Wiki markup has the same problem when exported to MS Excel. There's more information about this issue here: https://jira.atlassian.com/browse/JRA-14705.
Use JEditor CSV/TSV
Starting with JEditor 3.4.0, you can use JEditor CSV/TSV to export Jira issues without HTML tags in JEditor-enabled field values.
The feature is available on the Jira Search View screen:
When you click the JEditor CSV/TSV menu item, JEditor will export all issues from your current search to the CSV/TSV (tab-separated values) format. However, JEditor will only export the currently visible fields; there's no option to export all fields.
When exporting, JEditor will remove all HTML formatting from JEditor-enabled field values to keep the exported results readable.
Export to PDF instead of Excel
You can export to PDF. This will keep all visuals, including rich formatting, images, links.
JIRA PDF View plugin supports JEditor-enabled fields:
JEditor also provides a free PDF export option. You can find it on the Issue Search screen (only in the List view). This feature is simplistic compared to other export options and can only export columns visible on the Issue Search screen (it prints the issue table using the browser's print to PDF function).
Remove HTML tags after export (using Excel find and replace)
One more workaround is to remove all tags after exporting data to MS Excel. Select all columns that contain HTML tags and then find all tags using the wildcard character - "<*>" and replace them with the empty string.