Born in Mauchline, Ayrshire in 1765, Jean Armour was second oldest of the eleven children of stonemason James Armour (died 1798) and Mary Smith. She met Robert Burns on a "drying green" in Mauchline around 1784 when she chased his dog away from her laundry. According to Armour's testimony in 1827, she met Burns again at a local dance and she "fell acquainted" with him.

Jean became pregnant with twins early in 1786. Her announcement, in March 1786, that she was expecting Robert Burns' twins caused her father to be "in the greatest distress, and [he] fainted away". Burns signed a paper attesting his intent to marry Jean, but her father disapproved of the union.

James Armour destroyed the "certificate of informal marriage agreement" between Robert and Jean and he removed his daughter to Paisley to prevent a local scandal. However, word had spread and the Mauchline Kirk recalled her on 10 June 1786 to admit that she was unmarried and pregnant and to confirm the father's name. Burns was called by the Mauchline Kirk on 25 June 1786 and admitted his part in the affair.

His letters from this period indicate that he intended to marry Jean Armour as soon as they realized she was pregnant, but had been discouraged by her reluctance to disobey her father. By this time Burns was romantically involved with 'Highland' Mary Campbell (1763 - 1786) and she was also pregnant. They were considering a move to Jamaica. The emigration fell through and Mary died in October 1786 before she could give birth.

Believing he had been abandoned by Jean Armour, he set about having himself declared single. Jean's father, James Armour issued a warrant against him and Burns went into hiding.

Jean remained with her parents in the village of Mauchline, Robert was hiding out at the farm at Mossgiel. The couple continued to live apart even after the birth of their twins Robert and Jean, born 3 September 1786. Following the success of The Kilmarnock Edition, Burns temporarily moved to Edinburgh. He returned intermittently to Mauchline, during which time Jean became pregnant again.

When Burns returned permanently on 23 February 1788 he found Jean was destitute and had been expelled from the family home. They reconciled their relationship, and Burns found her a place to stay. On 3 March 1788 she went into labor and delivered a second set of twins, two girls, one of whom died on 10 March 1788, the other on 22 March 1788.

In the light of Burns's new-found celebrity as a poet, James Armour relented and allowed his daughter to be married to him. Although their marriage was registered on 5 August 1788 in Mauchline, the parish records describe them as having been "irregularly married some years ago". She and Burns moved to Ellisland Farm where they stayed until 1791 when they moved to Dumfries, where both would live for the rest of their lives.

Jean Armour and Robert Burns had nine children together (he had at least another four by other women), the last of whom was born on the day of his funeral in July 1796.

Her widowhood and the straitened circumstances she found herself in after Burns's death attracted national attention and a charitable fund was collected for her and the children. She survived her husband by 38 years, and lived to see his name become celebrated throughout the world. Twenty years after his death, his fame had reached such a point that his remains were removed from their modest grave in St Michael's Kirkyard, Dumfries, and placed in a specially commissioned mausoleum. Here, Jean Armour was buried when she died in 1834. Statues of Jean were erected in Mauchline in 2002, and in Dumfries, opposite St Michael's Kirk, in 2004.