The Suppress user right grants the ability to do a special kind of revision deletion called suppression by ticking "Apply these restrictions to Sysops and lock this interface" which hides the revision from admins as well as other users, and produces a log message in the private suppression log instead of the public deletion log which only other suppressors can see.
Additionally, suppress can be used to hide a username that is grossly inappropriate from Special:ListUsers at the same time as indefinitely blocking them. This feature will also suppress the username from most logs and edits, although the username may still be visible in some places, such as rollback edit summaries.
This right is typically only granted to Stewards and System Administrators. Suppress should usually only be used to remove personal information, copyright infringement, serious personal attacks, or other grossly insulting material, but there might be exceptions, depending on the discretion of the suppressor. Except in these cases, standard revision deletion should be used. This is one of the six default MediaWiki user groups, see mw:Help:User rights and groups.