vedān uddharate jaganti vahate bhū-golam udbibhrate
daityaḿ dārayate baliḿ chalayate kṣatra-kṣayaḿ kurvate
paulastyaḿ jayate halaḿ kalayate kāruṇyam ātanvate
mlecchān mūrchayate daśakṛti-kṛte kṛṣṇāya tubhyaḿ namaḥ
O Lord Krsna, I offer my obeisances unto You, who appear in the forms of these ten incarnations. In the form of Matsya You rescue the Vedas, and as Karma You bear the Mandara Mountain on Your back. As Varaha You lift the earth with Your tusk, and in the form of Narasimha You tear open the chest of the daitya Hiranyakasipu. In the form of Vamana You trick the daitya king Bali by asking him for only three steps of land, and then You take away the whole universe from him by expanding Your steps. As Parasurama You slay all of the wicked ksatriyas, and as Ramacandra You conquer the raksasa king Ravana. In the form of Balarama You carry a plow with which You subdue the wicked and draw toward You the River Yamuna. As Lord Buddha You show compassion toward all the living beings suffering in this world and at the end of the Kali-yuga You appear as Kalki to bewilder the mlecchas [degraded low-class men].
The Supreme Personality of Godhead, the Lord of all the spiritual and material universes and the cause of all causes, appears in various different incarnations for various different purposes. He appears as the Yuga avatars to establish the Yuga dharma of each age, He appears as Vyas dev to compile the vedic literatures which teach one about the Supreme Personality of Godhead, He comes as various incarnations in order to reestablish the proper social order in the society, He comes in the forms of Narayan Rishi, Kapil dev and various other incarnations to teach the people about self realisation, and most importantly, He appears in various forms as Ram, Narasimha, Vaman and others to perform sweet pastimes for the pleasure of his devotees and to attract the conditioned living entities to him through these various enchanting pastimes. Of these pastime incarnations, ten are most prominent and are known as the Dasa Avatar. However, although all these forms of the Lord are one and the same for they are all the incarnations of the Lord, yet, the fountainhead of them all and the source of all these forms of the Lord is Sri Krishna. This has been accepted by all the authorities and various statements in the Vedas proclaim Sri Krishna to be the Supreme and the source of all the various personalities of Godhead. In the Brahma samhita it has been said by Lord Brahma:
īśvaraḥ paramaḥ kṛṣṇaḥ sac-cid-ānanda-vigrahaḥ anādir ādir govindaḥ sarva-kāraṇa-kāraṇam Krsna who is known as Govinda is the Supreme Godhead. He has an eternal blissful spiritual body. He is the origin of all. He has no other origin and He is the prime cause of all causes.
This has also been confirmed numerous times by Sri Krishna himself in the Bhagavat Gita and explained by Shukadev Goswami in the Srimad Bhagwatam. In the famous Dashavatar Stotra composed by Srila Jayadev Goswami also he has mentioned in the shloka quoted at the beginning that all these are the incarnations of Sri Krishna. Although eternally engaged in the most enchanting pastimes in Goloka Vrindavan, Sri Krishna appears in various other forms to perform various activities like protecting the devotees and annihilating the miscreants and, most importantly, attracting the souls bewildered by Maya and giving them an opportunity to understand their constitutional position as the servants of the Lord and go back home back to Godhead, in their eternal form full of knowledge and bliss, by taking to the path of Bhakti. He therefore comes in various forms and performs innumerable wonderful pastimes. Of these 10 incarnations are the most prominetn and are as follows, as written by Srila Jayadev Goswami, and often recited by Srila Prabhuad:
pralaya-payodhi-jale dhṛtavān asi vedaḿ
keśava dhṛta-mīna-śarīra jaya jagadīśa hare
O Kesava! O Lord of the universe! O Lord Hari, who have assumed the form of a fish! All glories to You! You easily acted as a boat in the form of a giant fish just to give protection to the Vedas, which had become immersed in the turbulent sea of devastation.
kṣitir iha vipulatare tiṣṭhati tava pṛṣṭhe
keśava dhṛta-kūrma-śarīra jaya jagadīśa hare
O Kesava! O Lord of the universe! O Lord Hari, who have assumed the form of a tortoise! All glories to You! In this incarnation as a divine tortoise the great Mandara Mountain rests upon Your gigantic back as a pivot for churning the ocean of milk. From holding up the huge mountain a large scar like depression is put in Your back, which has become most glorious.
vasati daśana-śikhare dharaṇī tava lagnā
śaśini kalańka-kaleva nimagnā
keśava dhṛta-śūkara-rūpa jaya jagadīśa hare
O Kesava! O Lord of the universe! O Lord Hari, who have assumed the form of a boar! All glories to You! The earth, which had become I,merged in the Garbhodaka Ocean at the bottom of the universe, sits fixed upon the tip of Your tusk like a spot upon the moon.
tava kara-kamala-vare nakham adbhuta-śṛńgaḿ
keśava dhṛta-narahari-rūpa jaya jagadīśa hare
O Kesava! O Lord of the universe! O Lord Hari, who have assumed the form of half-man, half-lionl All glories to You! lust as one can easily crush a wasp between one’s fingernails, so in the same way the body of the wasp like demon Hiranyakasipu has been ripped apart by the wonderful pointed nails on Your beautiful lotus hands.
chalayasi vikramaṇe balim adbhuta-vāmana
keśava dhṛta-vāmana-rūpa jaya jagadīśa hare
O Kesava! O Lord of the universe! O Lord Hari, who have assumed the form of a dwarf-brahmana! All glories to You! O wonderful dwarf, by Your massive steps You deceive King Bali, and by the Ganges water that has emanated from the nails of your lotus feet, You deliver all living beings within this world.
snapayasi payasi śamita-bhava-tāpam
keśava dhṛta-bhṛgupati-rūpa jaya jagadiśa hare
O Kesava! O Lord of the universe! O Lord Hari, who have assumed the form of Bhrgupati [Parasurama]! All glories to You! At Kuruksetra You bathe the earth in the rivers of blood from the bodies of I he demoniac ksatriyas that You have slain. The sins of the world are washed away by You, and because of You people are relieved room the blazing fire of material existence.
vitarasi dikṣu raṇe dik-pati-kamanīyaḿ
keśava dhṛta-rāma-śarīra jaya jagadiśa hare
O Kesava! O Lord of the universe! O Lord Hari, who haze assumed the form of Ramacandra! All glories to You! In the battle of Lanka You destroy the ten-headed demon Ravana and distribute his heads as a delightful offering to the presiding deities of the ten directions, headed by Indira. This action was long desired by all of them, who were much harassed by this monster.
vahasi vapuṣi viśade vasanaḿ jaladābhaḿ
keśava dhṛta-haladhara-rūpa jaya jagadiśa hare
O Kesava! O Lord of the universe! O Lord Hari, who have assumed the form of Balarama, the yielder of the prowl All glories to You! On Your brilliant white body You wear garments the color of a fresh blue rain cloud. These garments are colored like the beautiful dark hue of the River Yamuna, who feels great fear due to the striking of Your plowshare.
nindasi yajña-vidher ahaha śruti-jātaḿ
keśava dhṛta-buddha-śarīra jaya jagadīśa hare
O Kesava! O Lord of the universe! O Lord Hari, who have assumed the form of Buddha! All glories to You! O Buddha of compassionate heart, you decry the slaughtering of poor animals performed according to the rules of Vedic sacrifice.
mleccha-nivaha-nidhane kalayasi karavālaḿ
dhūmaketum iva kim api karālam
keśava dhṛta-kalki-śarīra jaya jagadīśa hare
O Kesava! O Lord of the universe! O Lord Hari, who have assumed the form of Kalki! All glories to You! You appear like a comet and carry a terrifying sword for bringing about the annihilation of the wicked barbarian men at the end of the Kali-yuga.
śrī-jayedeva-kaver idam uditam udāraḿ
śṛṇu sukha-daḿ śubha-daḿ bhava-sāram
keśava dhṛta-daśa-vidha-rūpa jaya jagadīśa hare
O Kesava! O Lord of the universe! O Lord Hari, who have assumed these ten different forms of incarnation! All glories to You! O readers, please hear this hymn of the poet Jayadeva, which is most excellent, an awarder of happiness, a bestower of auspiciousness, and it is the best thing in this dark world.