Abarim Publications' online Biblical Greek Dictionary
The particle δε (de) indicates a mild objection or simple transition and can sometimes be translated with "but" or "also". More often, however, it carries the mere force of a sentence's natural progression and as a result leaves little to be translated in English. Hebrew has a silent particle like that as well, albeit of slightly different function and origin: את ('et).
Our particle δε (de) frequently occurs with other particles in formulaic contexts: with μεν (men), which expresses affirmation, it forms a construct that means something like "indeed". With the copulative και (kai) it literally forms "and but" but takes on the meaning of "also".