In LATEX, two single quotes are used as double quotes. To help you insert these efficiently, Kile allows you to press " to insert two opening single quotes. Furthermore, if you want to close a quotation, you also have to press ". Kile will be smart enough to recognize this case and inserts two closing quotes for LATEX.
To get a literal double quote on the other side, press " twice.
You can enable or disable this auto insertion of opening and closing double quotes in section → → .
If you also include language-specific options
you will also be able to use German or French double quotes. Many more languages are available.