وَهُوَ الَّذِي يُنَزِّلُ الْغَيْثَ مِن بَعْدِ مَا قَنَطُوا
...
And He it is Who sends down the rain after they have despaired,
means, after the people have given up hope that rain will fall, He sends it down upon them at their time of need.
This is like the Ayah:
وَإِن كَانُواْ مِن قَبْلِ أَن يُنَزَّلَ عَلَيْهِمْ مِّن قَبْلِهِ لَمُبْلِسِينَ
And verily, before that (rain) -- just before it was sent down upon them -- they were in despair! (30:49)
...
وَيَنشُرُ رَحْمَتَهُ
...
and spreads His mercy.
means, He bestows it upon all the people who live in that region.
Qatadah said, "We were told that a man said to Umar bin Al-Khattab, may Allah be pleased with him, `O Commander of the faithful, no rain has come and the people are in despair.'
Umar, may Allah be pleased with him, said,
`Rain will be sent upon you,' and he recited:
وَهُوَ الَّذِي يُنَزِّلُ الْغَيْثَ مِن بَعْدِ مَا قَنَطُوا وَيَنشُرُ رَحْمَتَهُ
وَهُوَ الْوَلِيُّ الْحَمِيدُ
And He it is Who sends down the rain after they have despaired, and spreads His mercy. And He is the Protector, Worthy of all praise."
Meaning He is the One Who is in control of His creation, taking care of what will benefit them in this world and the Hereafter, and the consequences of all His decrees and actions are good, for which He is worthy of all praise.