After placing ourselves within the intimate confines of Allah’s refuge by saying أعوذ باللهِ we then proceed to mention that from which we have taken refuge and wish to be protected from: الشيطان الرجيم usually translated as ‘the accursed shaytan’ but taking a deeper look at the meanings of these words can give us a better understanding of them.
The word شيطان comes from the root ش ط ن which means “to be distant or remote,” and the Shaytaan was so-called because he became distant and remote from the truth and from the mercy of Allah, and thus from all good.
The word رجيم is an adjective for the word شيطان and refers to one who is cast at [usually with stones], or who himself casts stones at others, with the purpose of driving them away. So the shaytan stones others with temptations and drives them to sins, to drive them away from good and from Allah’s mercy. And He himself has been cast with the curse of being distanced from the Mercy of Allah.
This phrase beautifully juxtaposes the intimacy and closeness of being within the confines of the safe and protective space that is Allah’s refuge, with the vast distance and remoteness at which we wish to keep the shaytan - the one who himself is far removed and distant from all good, and it is this meaning that we are essentially saying when we proclaim, أعوذ باللهِ من الشيطانِ الرجيم.