The only way to reliably delete specific rows from a database, is to have a unique property (id) for each row. Names are not necessarily unique. Worse, you may have double entries. If you try to delete a double of a row by user name using the name as identifier for the row, for example, that will result in both rows to be deleted. Not what you want.

Deleting a row by ID is easy:

DELETE FROM users WHERE id=?
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As for more than one row, databases start to digress. Some give you the option to use IN(1,2,3)... but personally, I'd just delete them one by one in a loop. It's not like that would take such a long time: typically a small query will execute in a few milliseconds.

As you didn't say what kind of interface you're using, I can't go into much more details. In a HTML form you typically use the same name for every checkbox, and the id as the value. Then, for every checked checkbox, you'll get a parameter checkboxname=rowid. It's easy to loop through those.