The poet of this ghazal is Mirza Ghalib, who is known for his great literature (poems). He has big name in Urdu Poetry. You can read his all poems here – https://rekhta.org/ghazals/hazaaron-khvaahishen-aisii-ki-har-khvaahish-pe-dam-nikle-mirza-ghalib-ghazals

This ghazal has been sung by many singers till now, in their own style and tune. My personal favourite is of Jagjeet Singh. He has both composed and sung this ghazal with great tune. This is very silent and gives peace of mind.

Jagjeet Singh –

1. Original song from the Movie –

2. Live Performance –

In this live Ghazal performance, Jagjeet Singh explains the meaning of ghazal as well.

The rendition of this ghazal has been sung by many other singers in their own way, that includes singers like Abida Parveen, Lata Mangeshkar, Anuradha Paudwal, Ghulam Ali, etc.

Meaning of the ghazal –

Hazaaron khwahishen aisi ke har khwahish pe dam nikle
Bohat nikle mere armaan, lekin phir bhi kam nikle
 
[khwaish = desire]
I have thousands of desires, which are such that each one of them is capable of driving every possible life out of me. That’s the translation of the first line, but what follows leaves you ecstatic. He says, my some desires were fulfilled, or came out (the literal translation of the word ‘nikle’), but still some were left unfulfilled. What a way of expressing the thought that my desires were left unfulfilled.
 
Nikalna khuld se aadam ka soonte aaye hain lekin
Bahot be-aabru hokar tere kooche se hum nikle
 
[khuld = heaven ; aabru = fame/honor ; kooche = street]
This relates to the story of Adam when he was thrown out of heaven. In the same way he relates his situation of being thrown out disrespectfully from the house (comparing it to heaven) to that of Adam. 
 
Mohabbat mein nahin hai farq jeenay aur marnay ka
Usi ko dekh kar jeetay hain, jis kaafir pe dam nikle
 
[kaafir = non-believers]
In love, there is no difference between living and dying. I began to live only after I saw her, that infidel over whom the breadth will depart.
Hazaaron khwahishen aisi ke har khwahish pe dam nikle
Bohat niklay mere armaan, lekin phir bhi kam nikle
Khuda ke waaste parda na kaabe se uthaa zaalim
Kaheen aisa na ho yaan bhi wahi kaafir sanam nikle
For God’s sake, don’t remove the veil off of the Kaaba the tyrant. What if my deceitful lover hides behind it?
 
Kahaan maikhane ka darwaaza Ghalib aur kahaan vaaiz
Par itna jaantay hain kal voh jaata tha ke ham nikle
 

[maikhana = place wher alcohol is serverd ; vaiz = preacher]

The preacher and the bar’s entrance are way apart, yet I saw him entering the bar as I was leaving.
More explanation – 
The preacher says that drinking is bad and its a sin. But despite all his teachings of abstinence, he too drinks. This is what the literal meaning is.. and it implies that addiction to wine is universal..while people like Ghalib admit what they do. The preacher does not. He pretends that he does not need alcohol, while even he can’t resist it.
 
Hazaaron khwahishen aisi ke har khwahish pe dam nikle
Bohat niklay mere armaan, lekin phir bhi kam nikle..
Source: Snex.in