Verse 17 and 18 explains what this nearness means :
Yusuf Ali:
[050:016] It was We Who created man, and We know what dark suggestions his soul makes to him: for We are nearer to him than (his) jugular vein.
[050:017] Behold, two (guardian angels) appointed to learn (his doings) learn (and noted them), one sitting on the right and one on the left.
[050:018] Not a word does he utter but there is a sentinel by him, ready (to note it).
Shakir:
[050:016] And certainly We created man, and We know what his mind suggests to him, and We are nearer to him than his life-vein.
[050:017] When the two receivers receive, sitting on the right and on the left.
[050:018] He utters not a word but there is by him a watcher at hand.
Pickthall:
[050:016] We verily created man and We know what his soul whispereth to him, and We are nearer to him than his jugular vein.
[050:017] When the two Receivers receive (him), seated on the right hand and on the left,
[050:018] He uttereth no word but there is with him an observer ready.