The Meaning of Ar-Rajim
Ar-Rajim means, being expelled from all types of righteousness. Allah said,
[وَلَقَدْ زَيَّنَّا السَّمَآءَ الدُّنْيَا بِمَصَـبِيحَ وَجَعَلْنَـهَا رُجُوماً لِّلشَّيَـطِينِ]
(And indeed We have adorned the nearest heaven with lamps, and We have made such lamps Rujuman (as missiles) to drive away the Shayatin (devils)) (67:5).
Allah also said,
[إِنَّا زَيَّنَّا السَّمَآءَ الدُّنْيَا بِزِينَةٍ الْكَوَكِبِ - وَحِفْظاً مِّن كُلِّ شَيْطَـنٍ مَّارِدٍ - لاَّ يَسَّمَّعُونَ إِلَى الْمَلإِ الاٌّعْلَى وَيُقْذَفُونَ مِن كُلِّ جَانِبٍ - دُحُوراً وَلَهُمْ عَذابٌ وَاصِبٌ - إِلاَّ مَنْ خَطِفَ الْخَطْفَةَ فَأَتْبَعَهُ شِهَابٌ ثَاقِبٌ ]
(Verily, We have adorned the near heaven with the stars (for beauty). And to guard against every rebellious devil. They cannot listen to the higher group (angels) for they are pelted from every side. Outcast, and theirs is a constant (or painful) torment. Except such as snatch away something by stealing, and they are pursued by a flaming fire of piercing brightness) (37:6-10).
Further, Allah said,
[وَلَقَدْ جَعَلْنَا فِى السَّمَاءِ بُرُوجًا وَزَيَّنَّـهَا لِلنَّـظِرِينَ - وَحَفِظْنَـهَا مِن كُلِّ شَيْطَـنٍ رَّجِيمٍ - إِلاَّ مَنِ اسْتَرَقَ السَّمْعَ فَأَتْبَعَهُ شِهَابٌ مُّبِينٌ ]
(And indeed, We have put the big stars in the heaven and We beautified it for the beholders. And We have guarded it (near heaven) from every Shaytan Rajim (outcast Shaytan). Except him (devil) who steals the hearing then he is pursued by a clear flaming fire.) (15:16-18).
There are several similar Ayat. It was also said that Rajim means, the person who throws or bombards things, because the devil throws doubts and evil thoughts in people's hearts. The first meaning is more popular and accurate.