Jacobethan Revival architecture refers to the revival of English Renaissance architecture, popular beginning in England in the 1820s and persisting until a century later. It incorporates classical and Gothic/Tudor motifs. I tend to use it as a catch-all for vaguely Tudor/Renaissance architecture that doesn't fit neatly in the Gothic Revival, Tudor Revival, or Renaissance Revival styles.
The term "Jacobethan" is a portmanteau of "Jacobean" and "Elizabethan" (the two predominant eras of Renaissance architecture in England) coined by historian John Betjeman in 1933. He wrote that they were incorrectly labeled in terms of dominance of a specific style, e.g. classical features predominating Gothic ones in Jacobean architecture, and united the two to avoid confusion.
Though the style is identified as having begun in the 1820s, it did not become prominent until 1835, when the design competition for the new House of Parliament asked for Gothic and Elizabethan proposals. Additionally, English Renaissance architecture was romanticized by architects and clients alike during the early Victorian era. The style remained popular through the turn of the 20th century, and it spread to Canada and the United States by that time.
Jacobethan Revival architecture includes both Renaissance and Gothic features. Examples of the former include columns, pilasters, balustrades, and symmetrical massing/organization. The Gothic influence can be seen in the fenestration, oriel windows, brickwork, and towers/spires. The end result is a unique hybrid of the two styles.