If one checks most tafsir books he finds that apparently, there's not really much to say about this verse (ibn Kathir even doesn't explain the verse at all), only the fiqh dispute whether it is a verse which requires sujud or not is widely discussed so among those who said no are the Imams abu Hanifa, Malik (in al-Muwatta' and al-Mudawanah) and Sufyan at-Thawri. One of the hadith which the others (and they seem to be the majority) relay on is this hadith with the weak narrator abu-Lahi'ah, as even at-Tirmdihi quoted. Details about the madhab views could be found in my answer here.
Ibn Achour in his tafsir (at-tahrir wa-tanwir) pointed to the fact that most of this surah is addressing the disbelievers while the end verses finally come to address the believers and he said the meaning of
Bow down, prostrate yourselves
is the order to pray or referred to the prayer (salat) as it is the most important worship ...
and adore your Lord;
is underlining the importance of the prayer again. And what is meant by worship or adoring our Lord are the other worships like fasts and hajj ...
Al-Bagahwi commented the statement as follows: (adore "only" your Lord).
"and do good,"
refers to zakat and good behavior towards others like maintaining the ties of kinship, Enjoining what is good and forbidding what is evil ...
Imam at-Tabari said about the last two statements: submit to your lord and serve him with humbleness.
that you may prosper.
is a promise to prosper (which can only mean that they might enter jannah) if they did these deeds well.
To conclude: This verse asks as to pray and submit to Allah by doing what he asks us and doing good deeds and Allah gives the promise that if we do it good we may do it right and good, we will come paradise or jannah nearer! As said in the comment of Sassir this should be a reason for us (believers) to thank Allah and prostrate, as not only he made a promise to us he also showed or guided us the way to prosper.
I hope this was helpful.
And Allah knows best!