Jtdcftul

ॐ पूर्णमदः पूर्णमिदं पूर्णात्पूर्णमुदच्यते।

पूर्णस्य पूर्णमादाय पूर्णमेवावशिष्यते॥

When I fed it to search engine, I get many explaination by different people according to their understanding. I want to know in what context originally it was written and what is its meaning.

I read it on front page of Ishavasyopnishad.

This is actually a Shanti Mantra (peace Mantra) from the Upanishads. It can be interpreted in different ways.

One translation from greenmesg.com is as follows:

ॐ पूर्णमदः पूर्णमिदं पूर्णात्पुर्णमुदच्यते
पूर्णस्य पूर्णमादाय
पूर्णमेवावशिष्यते ॥
ॐ शान्तिः शान्तिः शान्तिः ॥

Om Puurnnam-Adah Puurnnam-Idam Puurnnaat-Purnnam-Udacyate

Puurnnasya Puurnnam-Aadaaya Puurnnam-Eva-Avashissyate ||
Om
Shaantih Shaantih Shaantih ||

Meaning:

1: Om, That (Outer World) is Purna (Full with Divine Consciousness);
This (Inner World) is also Purna (Full with Divine Consciousness);
From Purna comes Purna (From the Fullness of Divine Consciousness the
World is manifested) , 2: Taking Purna from Purna, Purna Indeed
Remains (Because Divine Consciousness is Non-Dual and Infinite). 3: Om
Peace, Peace, Peace.

Here they have translated the this (idam) and that (adah) as inner/outer worlds.

In this answer I have used Adi Shankara's translation/interpretation, according to which, this= Nirguna Brahman (or Karana Brahman) and that= Saguna Brahman (or the Karya Brahamn). So, both are equally full or infinite is the meaning.

What is the reason Isha Upanishad is starting with that particular Mantra?

According to Muktika Upanishad, which is a minor Upanishad, various Upanishads will have particular Shanti Mantras associated with them.

The teacher starts the recital of an Upanishad after chanting that particular Shanti Mantra.

The text says that the Mantra "Purnamidam .." is the Shanti Mantra for 19 Upanishads that are attached to the Shukla Yajur Veda:

"That (which lies beyond) is full" [

ॐ पूर्णमदः पूर्णमिदं पूर्णात्पुर्णमुदच्यते पूर्णश्य पूर्णमादाय
पूर्णमेवावशिष्यते ॥ ॐ शान्तिः शान्तिः शान्तिः ॥

auṁ pūrṇamadaḥ pūrṇamidaṁ pūrṇātpurṇamudacyate pūrṇaśya pūrṇamādāya
pūrṇamevāvaśiṣyate || auṁ śāntiḥ śāntiḥ śāntiḥ ||

That (Brahman) is whole. This (jagat) is whole. From that (Brahman)
whole, this (jagat) whole has come. This (jagat) whole (in spite of)
having come from that (Brahman) whole, Whole (Brahman) alone remains.
Om Peace Peace Peace. ] - and so on:

This is the Shanti-mantra of the following Nineteen Upanishads,
forming part of the Śukla Yajur Veda:

1. 
   Īśa Upanishad
   
   


2. Brihadāraṇyaka Upanishad
   
   


3. Jabālā Upanishad
   
   


4. Hamsa Upanishad
   
   


5. Paramahamsa Upanishad
   
   


6. Subala Upanishad
   
   


7. Mantrika Upanishad
   
   


8. Niralamba Upanishad
   
   


9. Triśikhī-brāhmaṇa Upanishad
   
   



10. Maṇḍala-brāhmaṇa Upanishad
    




11. Advaya-Tāraka Upanishad
    



12. Paiṅgala Upanishad
    
    


13. Bhikṣu Upanishad
    
    


14. Turyātīta Upanishad
    
    


15. Adhyātma Upanishad
    
    


16. Tarasara Upanishad
    
    


17. Yājñyavalkya Upanishad
    
    


18. Satyayani Upanishad
    
    


19. Muktikā Upanishad

And, that's why you have found it at the start of in the Isa Upanishad. It will also be found at the start of the Brihad Aranyaka Upanishad.

The text also gives the list of 108 Upanishads attached to the 4 Vedas as well as that of the Mantras will be the corresponding Shanti Mantras for those Upanishads.

The Mantra "Om sahana vavatu ..", for example, is mentioned as the Shanti Mantra for the 32 Upanishads that are attached with Krishna Yajur Veda.

So, the Svetasvatara Upanishad will start with it.