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Subhadra was the daughter of Vasudev and his first wife Rohini Devi. She was believed to be much younger to Krishna and Balarama since she was born after Vasudeva was released from Kansa's prison, according to the epic.
When Subhadra becomes of age, Balarama suggests her as a bride to Duryodhana, who was his favourite pupil. Subhadra was going to chose Duryodhana as her husband in the self-choice ceremony according to the seminal work, Mahabharata . Krishna tells Arjuna that he should forcibly take her away as there was no certainity that she would chose Arjuna at the self choice ceremony.
The quotation from Mahabharata : Subhadra Harna Parva :
Vasudeva answered, 'O bull amongst men, self-choice hath been ordained for the marriage of Kshatriyas. But that is doubtful (in its consequences), O Partha, as we do not know this girl's temper and disposition. In the case of Kshatriyas that are brave, a forcible abduction for purposes of marriage is applauded, as the learned have said. Therefore O Arjuna, carry away this my beautiful sister by force, for who knows what she may do at a self-choice.—quote
Vyasa's Mahabharata states that Subhadra was kidnapped by Arjuna. She was going to chose Duryodhana as her husband in Swayamvara which her brother, Balrama was going to organize. Arjuna was in the midst of self-imposed pilgrimage, for breaking terms of the agreement he had had with his brothers regarding private time with their common wife, Draupadi. He reached the city Dwaraka and meets Krishna with whom he spends time. Later he attends a festival held at Raivata mountain alongside Krishna. Other Yadava women including Subhadra was also there to see the festival. After seeing Subhadra, Arjuna is smitten by her beauty and wishes to marry her. But Krishna fears that she would choose Duryodhana as her husband, if a Swayamvara is held. So Krishna advises Arjuna to Kidnap Subhadra saying in the case of Kshatriyas that are brave, a forcible abduction for purposes of marriage is applauded, as the learned have said. Thus, Arjuna abducts Subhadra. But Balrama and other Yadavas are angered by this and decide to to pursue Arjuna. But they are dissauded by Krishna from attacking Arjuna. Finally, Balrama consents and conduct the marriage of Subhadra with Arjuna. 
The quotation from Mahabharata : Subhadra Harna Parva :
When that delightful festival of immense grandeur commenced, Vasudeva and Partha went about together. While wandering there, they saw the handsome daughter of Vasudeva, Bhadra by name, in the midst of her maids. As soon as Arjuna beheld her he was possessed by the god of desire. If this thy sister, this maid of the Vrishni race, becometh my wife, truly may I win prosperity in everything. Tell me, O Janardana, by what means I may obtain her. To get her I will achieve anything that is achievable by man.' "Vasudeva answered, 'O bull amongst men, self-choice hath been ordained for the marriage of Kshatriyas. But that is doubtful (in its consequences), O Partha, as we do not know this girl's temper and disposition. In the case of Kshatriyas that are brave, a forcible abduction for purposes of marriage is applauded, as the learned have said. Therefore O Arjuna, carry away this my beautiful sister by force, for who knows what she may do at a self-choice. Meanwhile Subhadra, having paid her homage unto that prince of hills, was coming towards Dwaravati. The son of Kunti, afflicted with the shafts of the god of desire, suddenly rushed towards that Yadava girl of faultless features and forcibly took her into his car. Having seized that girl of sweet smiles, that tiger among men proceeded in his car of gold towards his own city (Indraprastha).—quote
At a later time period, inspired from folk tales, certain movies, television serials like B.R. Chopra's Mahabharat (1988 TV series) and the recent Mahabharat (2013 TV series) portrayed an alternate story in which Subhadra kidnaps Arjuna and that she was in love with him. According to this story, Subhadra heard about Arjuna and his valiant deeds and began to admire Arjuna secretly. Arjuna during his exile reached Dwaraka and there chance upon Subhadra and the two secretly does a Gandharva Vivaha. Later with the help of Krishna the two leave for Indraprastha & while on the chariot Krishna advises Subhadra to be the charioteer which will show her consent to the pursuing Yadavas. Krishna pacifies Yadavas and Balrama. Researchers believe that this story gained popularity due to the rarity of the situation narrated in the story, ie, kidnapping of a male by a female. 
Subhadra and Arjuna had only one son, Abhimanyu. . He studied under the tutelage of Balarama, Krishna, Kritvarma and Pradyumna. Later he married Uttara and had a son named Parikshit. Abhimanyu died in the Kurukshetra war. Parikshit becomes the sole surviving heir of the entire Kuru dynasty. When he comes of age, the Pandavas appoint him as the king and goes for Vanaprastha in the Himalayas.
Certain sections of Hindus believe Subhadra to be a goddess named Yogmaya. Subhadra is one of the three deities worshipped at the Jagannath temple at Puri, along with Krishna (as Jagannatha) and Balarama (or Balabhadra). One of the chariots in the annual Ratha Yatra is dedicated to her. Apart from it she is also believed to be worshiped by certain communities in Odisha, West Bengal and Gujarat. 
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