दो लफ़्ज़ों की है, दिल की कहानी

"The tale of [two] hearts, is made of [only] two words ... love or youth."

If you interpret love or youth to mean true love or infatuation, you can see some justification in this simplified interpretation. It is said that Asha Bhonsle herself regards this song as one of her best renditions.

छूकर मेरे मन को, किया तूने क्या इशारा

"By touching my heart [or mind], what a gesture have you made?
This season changed, and the entire world seems lovely, wonderful."

Considering that an immensely desirable quality in a human being is to touch another at an emotional or at an intellectual level, it is only appropriate to have this quality immortalized in a song, crafted to hummable melody that only a Kishore Kumar can create.

अल्लाह तेरो नाम, ईश्वर तेरो नाम

This song brings out the secular nature of God, although only two forms of God are mentioned here:

1. Allah of the Muslim faith, 
2. Eswar of the Hindu faith. 

It also wishes for goodness in the world, in expressing that:

1. Everyone be blessed with good mind
2. Wives not lose their husbands. (This is probably a reflection of the time; women tended to be more dependent on men those days than nowadays).
3. Mothers' and sisters' not fulfilling their hopes
4. Life not be stifled by a [weak] body
5. Everyone be blessed with knowledge of God

The foregoing is nothing but an elaboration of another well-known Sanskrit phrase, वसुदैव कुटुम्बकं, or "The whole world is one family".

Above all, it is a beautiful rendering by the incomparable Lata Mangeshkar.