In L^AT_EX, 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 L^AT_EX.

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 Settings → Configure Kile... → LaTeX.

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If you also include language-specific options like ngerman or french, you will also be able to use German or French double quotes. Many more languages are available.