Ar-Rajim means, being expelled from all types of righteousness. Allah said,

﴿ظˆظژظ„ظژظ‚ظژط¯ظ’ ط²ظژظٹظ‘ظژظ†ظ‘ظژط§ ط§ظ„ط³ظ‘ظژظ…ظژط¢ط،ظژ ط§ظ„ط¯ظ‘ظڈظ†ظ’ظٹظژط§ ط¨ظگظ…ظژطµظژظ€ط¨ظگظٹط­ظژ ظˆظژط¬ظژط¹ظژظ„ظ’ظ†ظژظ€ظ‡ظژط§ ط±ظڈط¬ظڈظˆظ…ط§ظ‹ ظ„ظ‘ظگظ„ط´ظ‘ظژظٹظژظ€ط·ظگظٹظ†ظگ﴾

(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,

﴿ط¥ظگظ†ظ‘ظژط§ ط²ظژظٹظ‘ظژظ†ظ‘ظژط§ ط§ظ„ط³ظ‘ظژظ…ظژط¢ط،ظژ ط§ظ„ط¯ظ‘ظڈظ†ظ’ظٹظژط§ ط¨ظگط²ظگظٹظ†ظژط©ظچ ط§ظ„ظ’ظƒظژظˆظژظƒظگط¨ظگ - ظˆظژط­ظگظپظ’ط¸ط§ظ‹ ظ…ظ‘ظگظ† ظƒظڈظ„ظ‘ظگ ط´ظژظٹظ’ط·ظژظ€ظ†ظچ ظ…ظ‘ظژط§ط±ظگط¯ظچ - ظ„ط§ظ‘ظژ ظٹظژط³ظ‘ظژظ…ظ‘ظژط¹ظڈظˆظ†ظژ ط¥ظگظ„ظژظ‰ ط§ظ„ظ’ظ…ظژظ„ط¥ظگ ط§ظ„ط§ظ‘ظŒط¹ظ’ظ„ظژظ‰ ظˆظژظٹظڈظ‚ظ’ط°ظژظپظڈظˆظ†ظژ ظ…ظگظ† ظƒظڈظ„ظ‘ظگ ط¬ظژط§ظ†ظگط¨ظچ - ط¯ظڈط­ظڈظˆط±ط§ظ‹ ظˆظژظ„ظژظ‡ظڈظ…ظ’ ط¹ظژط°ط§ط¨ظŒ ظˆظژط§طµظگط¨ظŒ - ط¥ظگظ„ط§ظ‘ظژ ظ…ظژظ†ظ’ ط®ظژط·ظگظپظژ ط§ظ„ظ’ط®ظژط·ظ’ظپظژط©ظژ ظپظژط£ظژطھظ’ط¨ظژط¹ظژظ‡ظڈ ط´ظگظ‡ظژط§ط¨ظŒ ط«ظژط§ظ‚ظگط¨ظŒ ﴾

(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,

﴿ظˆظژظ„ظژظ‚ظژط¯ظ’ ط¬ظژط¹ظژظ„ظ’ظ†ظژط§ ظپظگظ‰ ط§ظ„ط³ظ‘ظژظ…ظژط§ط،ظگ ط¨ظڈط±ظڈظˆط¬ظ‹ط§ ظˆظژط²ظژظٹظ‘ظژظ†ظ‘ظژظ€ظ‡ظژط§ ظ„ظگظ„ظ†ظ‘ظژظ€ط¸ظگط±ظگظٹظ†ظژ - ظˆظژط­ظژظپظگط¸ظ’ظ†ظژظ€ظ‡ظژط§ ظ…ظگظ† ظƒظڈظ„ظ‘ظگ ط´ظژظٹظ’ط·ظژظ€ظ†ظچ ط±ظ‘ظژط¬ظگظٹظ…ظچ - ط¥ظگظ„ط§ظ‘ظژ ظ…ظژظ†ظگ ط§ط³ظ’طھظژط±ظژظ‚ظژ ط§ظ„ط³ظ‘ظژظ…ظ’ط¹ظژ ظپظژط£ظژطھظ’ط¨ظژط¹ظژظ‡ظڈ ط´ظگظ‡ظژط§ط¨ظŒ ظ…ظ‘ظڈط¨ظگظٹظ†ظŒ ﴾

(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.