Hi margje,
The wordpress_redirection_404* table is a log of all the 404 errors that happen on your site, which the Redirection plugin has detected.
If you look at the “Tools/Redirection/404″(top link) page, you’ll see a list of problematic URLs and missing images etc. This list is useful for identifying pages/images that don’t go anywhere and are broken links (i.e. 404 Not Found). In terms of SEO, you should look to map old, out of date URLs, to point to new versions of posts/pages (if there is one).
To reduce the size of the table, you can use the top checkbox on the left of the “Tools/Redirection/404” page and then use the “Bulk Actions” (top left) to delete all of the selected 404s. You may have several pages to go through… if you scroll down, there is a “Delete All” button, at the botom of this page, under “Log Management”. ??
You may also want to change the dropdown to a shorter duration.
Go to the “Tools/Redirection/Options” page and select the 404 duration to be “No logs” or “1 day”.
Hope that helps.
*Note: the prefix of your table may be different.