Not a main Avataar and 21st Avataar in 24 Avataar.
It is believed that he was the Avataar of Shesh Naag. See also Lakshman as he was also the Avataar of Shesh Naag.

Bhaagvat Puraan says that Balaraam Jee is Vishnu's Avataar. Vishnu plucked His two hair strands - one black and one white. With black hair He appeared as Krishn and with white hair He appeared as Balaraam. But according to popular belief Balaraam is the Avataar of Shesh Naag. This is Shesh Naag's 2nd Avataar. First he came as Lakshman along with Raam in Tretaa Yug.

It is also said that when Vishnu decided to come on Prithvi as Krishn, Shesh Jee told Him that he wanted to to go with Him as His elder brother, because when he came with Him as His younger brother (Lakshman) He could not say anything to Him as he was only a younger brother to Him. If he would be His elder brother, at lease he will be able to command Him as he wished. Vishnu said "OK" and Shesh Jee came as Krishn's elder brother - although that is a different matter that even being elder brother Shesh Jee could not command Krishn. (Who can command the One who commands everybody?)

Balaraam Jee was the 7th son of Vasudev and Devakee. Bhagavaan Vishnu transferred him to Vasudev's another wife Rohinee's womb with the help of His Yog Maayaa to deceive Kans. There he was born as Balaraam. After Balaraam was transferred, Krishn came to Devakee's womb and was born as Krishn. He was married to King Raivat's son Kakudmee's daughter Revatee. This is an interesting event. Once King Kakudmee went to Brahmaa Jee to consult him about the prospective groom. Brahmaa Jee was enjoying the dance at that time. Kakudmee did not consider proper to disturb him, so he also stood there and continued to see the dance. It was only a few moments that he saw the dance, that Brahmaa Jee spotted him and asked him the purpose of his coming. He told him his purpose and suggested some names. Brahmaa Jee said - "Kakudmee, I think you have been standing here for a long time. the names you are taking they are already dead, even their children are also dead. 27 Chatur-Yug have passed since. At this time Dwaapar Yug is running on Prithvi, so the most appropriate groom for your daughter is only Balaraam. You go there and marry her to him."

Kakudmee came back to Prithvi and to his capital, he did not find his capital and the place was already taken by some other people. Even the whole world was changed. In Dwaapar Yug people were shorter. Revatee was very tall. When he married his daughter to Balaraam, he was shorter, so Balaraam Jee just pressed her a little and she became of his size. Vishnu Puraan, 4/11 says that he had two sons from her - Vishath and Ulmuk

His weapon were Hal (plow) and Moosal (pestle). Both Balaraam and Krishn grew up together in Nand Gaanv playing with Gop and Gopee. He also killed a few Daitya in his lifetime. Both lived together, but on most matters they differed and Balaraam had to agree with Krishn. Even in Mahaabhaarat war, they differed. Since Balaraam did not want to favor any side, he went on Teerth yaatraa (pilgrimage) for that period. there he heard that Kaurav had lost and only Duryodhan remains, so he came back and when he arrived at the scene, Bheem and Duryodhan were fighting each other. At that time also he did not like Bheem's breaking Gadaa rules - hitting on the thigh of Duryodhan. then Krishn had to present several pleas to behave like this.

A couple of important events of his life are that he killed Rukmee (Rukminee's brother), and he killed Soot Jee (Romharshan) when he was on his Teerth Yaatraa.

When his time came to leave Prithvi, he just sat near the mouth of a cave and soon turned into Shesh Naag and entered the cave.

* There are three Raam - Parashuraam, Shree Raam, and Balaraam. 
--Parashuraam is he who always carries a Parashu (Pharasaa or axe), that is why he is called Parashuraam.
--Shree Raam is He who came with His wife Lakshmee or Shree, that is why he is called Shree Raam. It is identified as the incarnation with bow and arrow.
--Balaraam was very mighty that is why he is called Balaraam. He is identified with Hal (Plow) in his hand. That is why he is called Haladhar also.

There are four Yug - Aadi Shesh or Anant has taken different Avataar in different Yug
"Anantah Prathamam Roopam, Tretaya Lakshmanascha Tathah
Dwaapare Balabhadrashcha Kalau Kashchit Bhavishyati"

The meaning of this Shlok -
"In Krit Yug (1st Yug) Aaadi Shesh was the Snake Bed of the Lord
In Tretaa Yug (2nd Yug) he was incarnated as Lakshmana, brother of Raam
In Dwaapar Yug (3rd Yug) he was incarnated as Balaraam, brother of Krishn, and
In Kali Yug (4th Yug) he was incarnated as Swami Ramanuja,
From the above verses it is clear that Swami Raamaanuj is the Avataar of Aadi Shesh