(Indeed whosoever purifies himself shall achieve success.) meaning, he purifies himself from despised characteristics and he follows what Allah has revealed to the Messenger ﷺ.
وَذَكَرَ اسْمَ رَبِّهِ فَصَلَّى
(And remembers the Name of his Lord, and performs Salah.) meaning, he establishes the prayer in its appointed time, seeking the pleasure of Allah, obedience to His command, and implementation of His Law. We have already reported from the Commander of the believers, `Umar bin `Abdul-`Aziz, that he used to command the people to give the Sadaqat Al-Fitr, and he would recite this Ayah:
قَدْ أَفْلَحَ مَن تَزَكَّىٰ (Success is surely achieved by him who purifies himself,..87:14) The word tazakka is derived from zakah, the primitive meaning of which is 'to purify'. The zakah of wealth is so called because it purifies the rest of man's wealth for him. In this context, the word tazakka is used in a general sense, which comprehends the purity of faith and character, and purity of wealth.
وَذَكَرَ اسْمَ رَبِّهِ فَصَلَّىٰ (and pronounces the name of his Lord, then offers prayer....87:15). This covers all categories of prayer, obligatory as well as supererogatory. Some commentators say that it refers especially to Id prayers. This interpretation too can fall under the preceding category.
It is quite evident that there is planning in the creation of man and the world. This planning strongly implies that there must be some purpose behind this creation. And indeed, this purpose has been revealed to man through divine revelation. However, only that individual learns a lesson from revelation who is of a receptive nature. Such people will be introduced to the eternal bounties of God. But those whose arrogance prevents them from accepting guidance, will be doomed to being cast into the flames of the eternal fire.
Uthmani text of the Madinah mushaf (King Fahd Complex). Translation: Saheeh International. Tafsir via Quran.com.