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This verse was revealed when the Prophet (ﷺ) received the order to emigrate from Mecca to Medina. So here he (ﷺ) is praying to leave Mecca honourably and enter Medina honourably. It can also apply to any worldly activity that a person starts and finishes.
All prayer must be for Allah's aid and authority. However much we may plan, our success must depend on His aid. However nobler our motives, we have no right to imperil any lives unless there is authority in the Word of Allah. The Prophet only acts on Allah's commission and inspiration.
The entry and exit here referred to may be interpreted in four senses: (1) entry into death and exit at the resurrection: for the righteous, who have purified their souls by prayer (last verse) and spiritual teaching from the Qur-an (next verse), there is on each occasion a fuller and fuller realisation and enjoyment of truth and honour: for those who are estranged from Allah, the effect is the opposite: the truth becomes bitter and there is ignominy and exposure instead of honour: (2) entry for the holy Prophet into the new life at Madinah, which was still in the womb of futurity, and exit from the life of persecution and the milieu of falsehood, which surrounded him in his native city of Makkah still given up to idolatry: (3) referring to the impending Hijrat again, the prayer may mean, "Let it be from pure motives of truth and spiritual honour, and not from motives of anger against the city of Makkah or its persecutors, or of ambition or worldly power from the city of Madinah, which was ready to lay everything at the Prophet's feet": (4) generally, entry and exit at every stage of life.