Summing up

SLOKAM 12:
Ichchaa Meena Vihaara Kachchapa Mahaa pOtrin Yadruchcha HarE:
Rakshaa Vaamana Rosha Raama KaruNaa Kaakutstha HElaa halin /
KreeDaa Vallabha Kalka Vaahana Dasaa kalkin iti prathyaham
Jalpantha: purushaa: punanthi bhuvanam puNyougha paNyaapaNaa: //

MEANING:
Oh! You, the one who -
(1) took the form of a fish by your own desire
(2) took the form of a tortoise for enjoying an under water sport
(3) took the form of a behemoth wild boar
(4) took the Lion-Human form and appeared all of a sudden
(5) took the form of a dwarf with the sole intent to protect
(6) took the form of a ferocious warrior with an ax
(7) took the form of Compassion personified
(8) took the form of a man playing and displaying a plough as a toy-weapon
(9) took the form of Lord KrishNa to enact your playful drama
(10) will take the form of a horse rider, with a sword in hand
Those who meditate on these forms of yours purify the world and are verily the purveyors of spiritual merit.

COMMENTS:
1. In the 12th Sloka Swami Desika gives a beautiful summing up of the various Avataras assigning unique epithets to each one of them. This has also been explained already in the respective Slokas.
(1) Matsaya Avatara = Ichchaa Meena
(2) Koorma Avatara = Vihaara Kachchapa
(3) Varaha Avatara = Mahaa pOtrin
(4) Nrisimha Avatara = Yadruchcha HarE:
(5) Vaamana Avatara = Rakshaa Vaamana
(6) Parasurama Avatara =Rosha Raama
(7) Sri Rama Avatara = KaruNaa Kaakutstha
(8) Balarama Avatara = HElaa halin
(9) Krishna Avatara = KreeDaa Vallabha
(10) Kalki Avatara = Kalka Vaahana Dasaa kalkin

2. How relevant are these Avataras in our lives today? We know that activity of all sentient beings and insentient things are influenced by the interplanetary forces and Sastras provide for their propitiation.

3. However, Mumukshus (Those who desire Moksham). Prapannas (Those who have done Saranagathi to Lord Narayana and Paramaikaantins (Those who resort to Narayana but do not seek even MOksham from Him) do not propitiate these planets (Navagrahas).

4. Swami Desika has provided through this Stotram, a viable alternative by which the same effects of Navagraha propitiation could be secured. Our Poorva Acharyas hold that this Stotram would make the favorable planets to yield more favorable results while the unfavorable planets would be compelled to become favorable.

5. In this context, elders used to correlate the Avataras with the planets as shown below:
(1) Matsaya Avatara = Ketu (The descending node)
(2) Koorma Avatara = Sani (Saturn)
(3) Varaha Avatara = Rahu (Ascending node)
(4) Nrisimha Avatara = Budha (Mercury)
(5) Vaamana Avatara = Guru (Jupiter)
(6) Parasurama Avatara =Sukra (Venus)
(7) Sri Rama Avatara = Surya (Sun)
(8) Balarama Avatara = Kulikan (Naaga)
(9) Krishna Avatara = Chandra (Moon)
(10) Kalki Avatara = General
It is a matter for scholars to do research whether this correlation has any basis and if so, to enlighten us in this regard.