As described in Srimad-Bhagavatam 1:3:23, in the nineteenth and twentieth incarnations the Lord advented Himself as Lord Balarama and Lord Krsna in the family of Vrsni [the Yadu dynasty].
Vasudeva and Nanda Maharaja were stepbrothers. Vasudeva's father, Surasena, married a vaisya girl, and from her Nanda Maharaja was born. Later, Nanda Maharaja himself married a vaisya girl, Yasoda. Therefore his family is celebrated as a vaisya family, and Krsna, identifying Himself as their son, took charge of vaisya activities. Balarama represents plowing the land for agriculture and therefore always carries in His hand a plow, whereas Krsna tends cows and therefore carries a flute in His hand.
Balarama, who has the same original form of Krsna, is Himself a cowherd boy in Vrndavana, and He also considers Himself to belong to the ksatriya race in Dvaraka. Thus His color and dress are different, and He is called a pastime form of Krsna.
During their Vrindaban lila, Krsna and Balarama enjoyed many transcendental pastimes, which are described in the 10th Canto of Srimad-Bhagavatam. Gargamuni performed the name-giving ceremony for Krsna and Balarama, who spent their early life enjoying playful childish activities, crawling and walking, stealing butter and breaking the pots.
During their pastimes with the cowherd boys in the forests of Vrinaban, Balarama and Krsna killed numerous demons like Aghasura, Dhenukasura and Pralambasura, many of whom were sent by the demon Kamsa to kill the brothers. Later, they traveled to Mathura where they killed Kamsa's wrestlers, brothers, and Kamsa himself. Afterwards, they battled Jarasandha, and jumped from a mountain Jarasandha had set fire to.
Next they entered Dvaraka, where Balarama killed Rukmi and broke the teeth of the King of Kalinga during a chess game. Baladeva later went to Gokula, and on Raivataka Mountain he killed the mischievous demon ape Dvivida.
Lord Baladeva went to Hastinapura, which he pulled with his plow due to the arrogance of the Kauravas. Later, he went touring holy places, and killed Romaharsana and Balvala. Rather than join the battle of Kuruksetra, he returned to Dvaraka. Later, he left with His wife Revati.
Bhaktivedanta Book Trust. Excerpted and paraphrased from text and purports of HDG A.C. Bhaktivedanta Swami Srila Prabhupada.