An old Earth ship classification covering the slow cargo haulers of the 22nd century, such as the Mayweather family's Horizon, and the ageing training vessel on which Christopher Pike was crippled.
In Star Trek: Enterprise the J-class is a type of Earth Cargo Service freighter, a long string of cargo modules behind a small crew section, capable of little more than warp 1.8. Families spend their lives aboard such ships. Travis Mayweather grew up on the ECS Horizon, and in the episode Horizon he goes home after his father's death and helps his brother Paul fend off alien raiders.
The designation is heard much earlier in the original series. In The Menagerie, Commodore Mendez explains that Fleet Captain Pike was inspecting cadets on an old class J starship when a baffle plate ruptured, and that he went in to drag the trainees out, suffering the delta-ray exposure that left him unable to move or speak.