In the late 18th century, James Watt, inventor of a version of the Steam Engine that made it practical for use in the industrial Revolution (and the man for which the SI unit of power, the watt, is named) introduced "horsepower" as a unit of power (that is to say, rate of energy over time). The unit was designed to help potential buyers reckon with the capacity of engines compared to a draft horse, which would be the closest comparison people would be familiar with.
Watt measured how much power a horse could provide by having it turn a mill wheel. Knowing the weight of the wheel, the distance of the circumference of the circle of travel, and measuring the number of rotations a horse could make in a single hour (at a pace it could sustain all work day), Watt defined a horsepower to be 33,000 foot-pounds per minute. And he could build engines that produced more power. This was before the advent of standardized measures.
There are many different versions of "horsepower" in the early twenty-first century, with different definitions, such as immaterial horsepower, metric horsepower, and electric horsepower. They are all within the same order of magnitude, and are seldom used for official, precise measures (watts are much more common for the purpose when precision and accuracy are required), so the distinction is effectively arbitrary. Horsepower is only really used in advertisement for heavy machinery, such as automobiles, and is usually used to compare within the category (e.g. this car's engine is almost twice as powerful as that car's engine).
In the early twenty-first century, actual comparison between horsepower and the power output of a horse is not really relevant, as most people do not interact with horses so frequently.. A biological system like an equine does not have a set, consistent output. In short bursts, they may be able to produce 15 horsepower worth of power. Over the course of a day, they can produce less than a single horsepower.
A rack-mounted server is a computer designed for the purpose of providing service to a large number of clients. This is distinct from computers designed for personal use (as PCs) or computers designed for specialized use in individual devises. Rack-mounted servers prioritize ruggedness against disruption and the ability to work with other computers in parallel for scaling increase in computational power (almost always computers of the same time physically mounted on the same racks, hence the name). They might not be capable or effective at generating graphics, and might not be set up with a graphical user interface. They are commonly used to support websites and web applications, or databases for entire companies. It is possible to use a rack-server on its own, but they usually are used in large arrays, working together in in concert.
As the above points out, the particular individual rack-server supports a horsepower worth of electricity, so it was placed on a horse as a visual pun. People in the early twenty-first century would NOT be able to recognize the particular specifications of a server rack off hand. Only with the added context of the specifications does the joke become apparent.
The fact the rack server was confused with a dvd player is not unexpected. Most people in the early twenty-first century do not encounter rack servers, and, if they do, it would be in the context of dozens of them all being placed on the same rack, not a single unit. While DVD players are far less common at the time of the above post, they were particularly prevalent in the 2000s, and enough people are old enough to consider them as an option.