(covers information from several alternate timelines)
The J-class was a starship design of Earth origin utilized by the Earth Cargo Service as a freighter. They were operated by captains with an Earth Cargo Authority license. These vessels had a history dating back to the early 22nd century, with one of the ships of the class, the ECS Horizon, commissioned in 2102. (ENT: "Broken Bow", "Fortunate Son", "Horizon")
The forward more maneuverable tug section of the J-class starship could separate from the large aft cargo module. These ships were capable of hauling loads of up to 30,000 metric tons. (ENT: "Horizon")
J-class ships were capable of maintaining a maximum speed of warp 2. When the cargo load was full, it was, however, only safe to travel at warp 1.5. The warp reactors were personally designed by Zefram Cochrane himself, and there were rumors that he personally signed the inside of each reactor casing. The inertial dampers aboard the J-class were far less advanced than that of later warp-capable vessels. As such, all passengers on a J-class freighter would have to hold on to handles when the ship went to warp, or else risk losing their balance. (ENT: "Horizon")
J-class ships were protected by polarized hull plating and armed with two forward-mounted plasma turrets. By the mid-22nd century, the original weapons were not powerful enough to protect the ships from the pirates they encountered. It was possible to upgrade them or to increase the original weapons' yield by rerouting the impulse relays and tapping power directly from the impulse engines. (ENT: "Fortunate Son", "Horizon")
Ships of the class
In the final draft script of "Horizon", the J-class was described thus; "It's a large [...] cargo ship comprised of several large, numbered CARGO MODULES strung together, and a CREW MODULE perched at its nose." The same scene description went on to specify, in a bracketed note, that the J-class was to look similar to the Y-class, but be "slightly more compact." A later scene description commented that the "Command Module [while alone] is a compact, maneuverable vessel."
Since the J-class was meant be an earlier design than the NX-class, the art department of Star Trek: Enterprise intended to make the workings of the ECS Horizon appear to be more primitive than those of Enterprise NX-01. "We wanted the instrumentation on the Horizon to be just a little clunkier," explained Michael Okuda. "We went with larger buttons – that just seemed to make it less advanced – [and] signage in this 'retro-stencil' look." (Star Trek: Communicator issue 144, p. 32)
The computer displays on the J-class were another concern. "We had to do a whole new set of bridge graphics for the Horizon," James Van Over recalled. This facilitated an experiment whereby the art department inverted the normally white-text-with-black-background format seen on the show. "We tried black letters on a white background and tried to keep the same look," Van Over clarified, "but made it look like it might be a step back for the interface, or a case where they set theirs differently." (Star Trek: Communicator issue 144, pp. 32 & 33)
Several J-class bridge situation boards and control panels were sold in the It's A Wrap! sale and auction.  In addition, several furniture items including a side chair, table and lamp from Mayweather's quarters,  a table from the galley,  and six swivel chairs from the bridge  were also auctioned off.
In the script of "Fortunate Son", this class was colloquially referred to, in dialogue, as "class-J". This reference was changed, though, so the class is consistently referred to as "J-class" in canon.