Huda here means the faith that resides in the heart, and only Allah is able to create it in the heart of the servants. Allah said,
إِنَّكَ لاَ تَهْدِى مَنْ أَحْبَبْتَ
Verily, you (O Muhammad ) guide not whom you like (Al-Qasas 56)
لَّيْسَ عَلَيْكَ هُدَاهُمْ
Not upon you (Muhammad ) is their guidance (Al-Baqarah 272)
مَن يُضْلِلِ اللَّهُ فَلاَ هَادِيَ لَهُ
Whomsoever Allah sends astray, none can guide him (Al-A’raf 186)
and
مَن يَهْدِ اللَّهُ فَهُوَ الْمُهْتَدِ وَمَن يُضْلِلْ فَلَن تَجِدَ لَهُ وَلِيًّا مُّرْشِدًا
He whom Allah guides, he is the rightly guided; but he whom He sends astray, for him you will find no Wali (guiding friend) to lead him (to the right path) (Al-Kahf 17)
Huda also means to explain the truth, give direction and lead to it. Allah, the Exalted, said,
وَإِنَّكَ لَتَهْدِى إِلَى صِرَٰطٍ مُّسْتَقِيمٍ
And verily, you (O Muhammad ) are indeed guiding (mankind) to the straight path (Allah’s religion of Islamic Monotheism) (Ash-Shuraa 52)
إِنَّمَآ أَنتَ مُنذِرٌ وَلِكُلِّ قَوْمٍ هَادٍ
You are only a warner, and to every people there is a guide (Ar-Ra’d 7)
and
وَأَمَّا ثَمُودُ فَهَدَيْنَٰـهُمْ فَاسْتَحَبُّواْ الْعَمَى عَلَى الْهُدَى
And as for Thamud, We showed and made clear to them the path of truth (Islamic Monotheism) through Our Messenger (showed them the way of success), but they preferred blindness to guidance (Fussilat 17)
testifying to this meaning.
Also, Allah said,
وَهَدَيْنَٰـهُ النَّجْدَينِ
And shown him the two ways (good and evil). (Al-Balad 10)
This is the view of the scholars who said that the two ways refer to the paths of righteousness and evil, which is also the correct explanation. And Allah knows best.
The root meaning of Taqwa is to avoid what one dislikes. It was reported that Umar bin Al-Khattab asked Ubayy bin Kab about Taqwa. Ubayy said, “Have you ever walked on a path that has thorns on it” `Umar said, “Yes.” Ubayy said, “What did you do then” He said, “I rolled up my sleeves and struggled.” Ubayy said, “That is Taqwa.”