The depart of people here is related with Allah’s(swt) word (That Day), meaning, the Day of Resurrection. On this day, they come apart and separated into two groups; a group in Paradise, and a group in the Hell. They depart from their graves to the account ground to see the results of their works. They will be either rewarded or punished.
The word (separated) indicates that they do not gather, they will disperse, each one has a destiny. This word (separated) is mentioned in another verse, but in another meaning:
﴾ لَيْسَ عَلَيْكُمْ جُنَاحٌ أَنْ تَأْكُلُوا جَمِيعًا أَوْ أَشْتَاتًا ٰ﴿
(There is no blame upon you whether you eat together or separately.) (An-Noor: 61)
That is because they were eating separately and do not eat together. The Arabic word is also used to refer to a big difference between two persons.
لِّيُرَوْا أَعْمَالَهُمْ (to be shown [the result of] their deeds): They will see their good and bad deeds. They will be shown what their senses have committed. The deeds cannot be seen, rather, what indicate them, that is the written of their deeds in the records. Allah (swt) says:
ٰ﴾ وَكُلَّ إِنسَانٍ أَلْزَمْنَاهُ طَائِرَهُ فِي عُنُقِهِ ۖ وَنُخْرِجُ لَهُ يَوْمَ الْقِيَامَةِ كِتَابًا يَلْقَاهُ مَنشُورًا % اقْرَأْ كِتَابَكَ كَفَىٰ بِنَفْسِكَ الْيَوْمَ عَلَيْكَ حَسِيبًا﴿
(And [for] every person We have imposed his fate upon his neck, and We will produce for him on the Day of Resurrection a record which he will encounter spread open. % [It will be said], “Read your record. Sufficient is yourself against you this Day as accountant.)
If we, in this world, document events by sound and picture, so how would it be of Allah (swt) recording for us? A human will see his deeds of every minute and moment of his life in a way that cannot be denied. Therein, he would be left to himself to hold accountable of him; his tongue and skin would testify of what he had earned, so it will be the greatest testimony.