tasmai bhavan haya-siras tanuvam hi bibhrad
veda-druhav atibalau madhu-kaitabhakhyau
hatvanayac chruti-ganams ca rajas tamas ca
sattvam tava priyatamam tanum amananti
Translation by His Divine Grace A. C. Bhaktivedanta Swami Srila Prabhupada:
My dear Lord, when You appeared as Hayagriva, with the head of a horse, You killed two demons known as Madhu and Kaitabha, who were full of the modes of passion and ignorance. Then You delivered the Vedic knowledge to Lord Brahma. For this reason, all the great saints accept Your forms as transcendental, untinged by material qualities.
Purport by His Divine Grace A. C. Bhaktivedanta Swami Srila Prabhupada:
The Supreme Personality of Godhead in His transcendental form is always ready to give protection to His devotees. As mentioned herein, the Lord in the form of Hayagriva killed two demons named Madhu and Kaitabha when they attacked Lord Brahma. Modern demons think that there was no life in the beginning of creation, but from Srimad-Bhagavatam we understand that the first living creature created by the Supreme Personality of Godhead was Lord Brahma, who is full of Vedic understanding. Unfortunately, those entrusted with distributing Vedic knowledge, such as the devotees engaged in spreading Krsna consciousness, may sometimes be attacked by demons, but they must rest assured that demoniac attacks will not be able to harm them, for the Lord is always prepared to give them protection. The Vedas provide the knowledge by which we can understand the Supreme Personality of Godhead (vedais ca sarvair aham eva vedyah). The devotees of the Lord are always ready to spread knowledge by which one may understand the Lord through Krsna consciousness, but the demons, being unable to understand the Supreme Lord, are full of ignorance and passion. Thus the Lord, whose form is transcendental, is always ready to kill the demons. By culturing the mode of goodness, one can understand the position of the transcendental Lord and how the Lord is always prepared to remove all obstacles on the path of understanding Him.
In summary, whenever the Lord incarnates, He appears in His original transcendental form. As the Lord says in Bhagavad-gita (4.7):
yada yada hi dharmasya
glanir bhavati bharata
tadatmanam srjamy aham
“Whenever and wherever there is a decline in religious practice, O descendant of Bharata, and a predominant rise of irreligion — at that time I descend Myself.” It is simply foolish to think of the Lord as being originally impersonal but accepting a material body when He appears as a personal incarnation. Whenever the Lord appears, He appears in His original transcendental form, which is spiritual and blissful. But unintelligent men, such as the Mayavadis, cannot understand the transcendental form of the Lord, and therefore the Lord chastises them by saying, avajananti mam mudha manusim tanum asritam: “Fools deride Me when I descend in the human form.” Whenever the Lord appears, whether as a fish, a tortoise, a hog or any other form, one should understand that He maintains His transcendental position and that His only business, as stated here, is hatva — to kill the demons. The Lord appears in order to protect the devotees and kill the demons (paritranaya sadhunam vinasaya ca duskrtam). Since the demons are always ready to oppose Vedic civilization, they are sure to be killed by the transcendental form of the Lord.