In The Name of Allah, The Most Merciful, The Bestower of Mercy.

After a mention of the Iman and guidance bestowed upon them by Allah, they (i.e. the young men) then addressed what their people were upon. Their people used to ascribe partners to Allah in worship, so they detested them and clarified that their (beliefs, acts of worship etc) were not based on certainty; rather they were upon extreme ignorance and misguidance. Allah said that the young men said:

هَـٰٓؤُلَآءِ قَوۡمُنَا ٱتَّخَذُواْ مِن دُونِهِۦۤ ءَالِهَةً۬‌ۖ لَّوۡلَا يَأۡتُونَ عَلَيۡهِم بِسُلۡطَـٰنِۭ بَيِّنٍ۬‌ۖ فَمَنۡ أَظۡلَمُ مِمَّنِ ٱفۡتَرَىٰ عَلَى ٱللَّهِ كَذِبً۬ا

These our people have taken for worship aliha (gods) other than Him (Allah). Why do they not bring for them a clear authority? And who does more wrong than he who invents a lie against Allah]. [18:15]

لَّوۡلَا يَأۡتُونَ عَلَيۡهِم بِسُلۡطَـٰنِۭ بَيِّنٍ۬‌ۖ

Why do they not bring for them a clear authority?

Meaning: Bring Hujjah [i.e. clear and overwhelming proofs that would show the correctness of what they are upon and the falsehood of their opponents] and Burhan [i.e. evidences that clarify and distinguish between truth and falsehood from every angle]; however they have no way of doing so, rather they only invent a lie against Allah and this is the greatest type of wrong doing. This is why Allah said that the young men said:

فَمَنۡ أَظۡلَمُ مِمَّنِ ٱفۡتَرَىٰ عَلَى ٱللَّهِ كَذِبً۬ا
And who does more wrong than he who invents a lie against Allah.

وَتَرَى ٱلشَّمۡسَ إِذَا طَلَعَت تَّزَٲوَرُ عَن كَهۡفِهِمۡ ذَاتَ ٱلۡيَمِينِ وَإِذَا غَرَبَت تَّقۡرِضُہُمۡ ذَاتَ ٱلشِّمَالِ وَهُمۡ فِى فَجۡوَةٍ۬ مِّنۡهُ‌ۚ ذَٲلِكَ مِنۡ ءَايَـٰتِ ٱللَّهِ‌ۗ مَن يَہۡدِ ٱللَّهُ فَهُوَ ٱلۡمُهۡتَدِ‌ۖ وَمَن يُضۡلِلۡ فَلَن تَجِدَ لَهُ ۥ وَلِيًّ۬ا مُّرۡشِدً۬ا

And you might have seen the sun, when it rose, declining to the right from their Cave, and when it set, turning away from them to the left, while they lay in the midst of the Cave. That is (one) of the Ayat (proofs, evidences, signs) of Allah. He whom Allah guides, is rightly guided; but he whom He sends astray, for him you will find no Wali (guiding friend) to lead him (to the right Path).

Allah protected them from the sun by facilitating for them a cave in which when the sun rose, it declined to the right away from it, and when it set, it turned away from it to the left, thus, its heat did not come into contact with them and harm their bodies.

وَهُمۡ فِى فَجۡوَةٍ۬ مِّنۡهُ‌ۚ

While they lay in the midst of the Cave.

Meaning, a spacious part of it, so that fresh air and breezes reaches them, stuffiness removed and not harmed by narrow space, especially that they were staying there for a prolonged period. This is one of Allah’s Signs that demonstrates His Power, His mercy for them, and the fact that He responded to their supplications and guided them even in these matters. This is why Allah said:

مَن يَہۡدِ ٱللَّهُ فَهُوَ ٱلۡمُهۡتَدِ‌ۖ
He whom Allah guides, is rightly guided

Meaning, there is no path to aattaining guidance except from Allah, because He is the One Who guides and directs a person to all the welfare in this life and the next.

وَمَن يُضۡلِلۡ فَلَن تَجِدَ لَهُ ۥ وَلِيًّ۬ا مُّرۡشِدً۬ا

But he whom He sends astray, for him you will find no Wali (guiding friend) to lead him (to the right Path).

Meaning, neither will you find a guiding friend for him to look after him in a manner that will bring about welfare for him nor guide him to good and success.

[An Excerpt from Tafseer As-Sadi. slightly paraphrased]