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.