Why is it necessary to burn incense stick while praying?
It is not completely necessary to burn incense sticks while praying. It has just become a traditionally followed practice. What is necessary is to create an environment of sweet fragrance and aroma made out of pure material (like natural products). Because that purifies the air and it helps higher beings and ethereal beings to roam there if you are calling them. It is because prāna (life air) is the food for all beings starting from animals to gods:
prāṇaṃ devā anu prāṇanti manuṣyāḥ paśavaśca ye prāṇo hi bhūtānāmāyuḥ tasmātsarvāyuṣamucyate [Tait Up - 2.3]
The gods live on breath, also men and animals. Prāna certainly is the life of all beings. Therefore prāna is called life of all.
As prāṇa acts as the food for the jivātmā, using incense sticks, dhupa, etc. through the aromatic air food is offered to them in various worships, puja and rituals. So it's not completely necessary to burn incense sticks while praying unless some god or higher being is going to come there in a subtle form. But anyway, burning incense stick is a good practice as it will at the least make the place of worship pleasant.
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