Jaehaerys succeeded his half-uncle Maegor Targaryen as king, a cruel tyrant who had been at war with the Faith for years. Jaehaerys was wise and diplomatic, and desired harmony between the Crown and the Faith for the good of the realm, so he negotiated a peaceful end to the Faith Militant uprising. Jaehaerys, together with his new Hand of the King, Septon Barth, reached an accord with the High Septon: the crown would grant an amnesty and swear to always defend the Faith, and in return, the Faith Militant would disband and the Faith would withhold condemnations of the incestuous practices of the Targaryens.
In the books
In the A Song of Ice and Fire novels, Barth is remembered as one of the best Hands of the King that the realm ever had, just as Jaehaerys I is remembered as possibly its best king. Together they did much to improve and strengthen the realm across four decades of peace and prosperity.
Barth was low-born, the son of a blacksmith. He eventually became a septon and served in a humble position overseeing the Red Keep's library, where he became one of the most learned men in Westeros. King Jaehaerys I raised him up to be his Hand of the King; Jaehaerys greatly loved his sister-wife Queen Alysanne, who was practically his co-ruler, but it is said that Barth was his greatest friend, who was also very skilled in his office, aiding Jaehaerys in all the great works of his reign. While Barth was very well-educated, he remained plain-spoken and approachable.
Barth greatly valued all knowledge and even took an interest in rare manuscripts from across the Narrow Sea which had survived the Doom of Valyria. From his translated readings he wrote several famous compendiums of his own on topics such as Magic and Dragons, leading some later writers to criticize that he was half a sorcerer (though of course, given that during Jaehaerys's reign living dragons were kept at the royal court, it wasn't that far-fetch for Barth to study them).
Barth's writings include several claims which later maesters dismiss as mere fantasy (i.e. believing that the White Walkers actually existed once), particularly in his book Dragons, Wyrms, and Wyverns: Their Unnatural History - considered one of the best recent works on dragon-lore. However, about sixty years after Jaehaerys's death the pious King Baelor I Targaryen ordered all of Barth's books hunted down and burned for containing wicked and unnatural knowledge.
A few precious fragments of Barth's writings survived Baelor's destruction order and they are of great value to those interested in topics such as dragons. Tyrion Lannister managed to gets his hands on a fragment about ten years before the main narrative. Maester Aemon was also well-versed in readings from the surviving fragments, knowledge he shared with Samwell Tarly. Aemon said that according to Barth, dragons can actually shift gender from female to male and back again, as the needs of the species require - other maesters are aware of this claim but dismiss it as fantastical.