Before I can answer this, it’s important to establish what legendaries are. For the most part, legendary pokémon are thought to be myths. They’re extremely rare to the point where it’s commonly thought that there are only one of each species in the world. Many of them are fantastically powerful, capable of manipulating the forces of nature themselves, if they aren’t simply embodiments of their respective elements. They are, in essence, kami—or, for lack of a better term in translation, what many would consider gods or simply spirits of nature themselves. Or in other words, the legendary pokémon transcend all other definitions of existence in terms of power and rarity.

Pseudo-legendaries are a step below that. These are the rarest pokémon from each region that we know are not unique. They are each able to evolve, and at the height of their evolutionary lines, pseudo-legendaries are capable of immense destructive force. This is in comparison to legendaries, who maintain a consistent level of power from birth (and thus do not need to evolve) and who aren’t simply strong but rather control nature. As strong as pseudo-legendaries may be, they can’t simply command nature on the level that legendaries can. Thus, a dragonite may be able to generate hurricane-force winds, but it can’t literally generate hurricanes the way lugia does.

On the other hand, as I’ve mentioned in above, legendaries are far rarer than ordinary pokémon. For example, up until recently, wild dratini colonies were thought to be a myth. If someone was lucky, maybe they might find a single dratini in their lifetime, but that was it. Then it was discovered that dratini colonies do exist, but they’re so rare and difficult to reach that only exceptional trainers can find them. Dratini otherwise breed only once in a decade (in the wild, anyway), which drastically limits their numbers. In short, a dratini is not something you simply stumble upon in the wild like you would an ekans. And dratini are one of the more common pseudo-legendaries. Beldum are even more ridiculous to find.

Of course, rarity isn’t the only thing that defines a pseudo-legendary, although it’s certainly one of the requirements. Again, power is another factor. While a Rock Slide may be devastating in the hands of an aggron, it’s far more devastating in the hands of a tyranitar. Likewise, metagross and goodra both can withstand far more damage than most ordinary pokémon, and salamence and garchomp are far faster. In short, the pseudo-legendaries are collectively stronger across the board—that is to say, offensively, defensively, and in terms of speed—than most ordinary pokémon.

Granted, yes, it’s true that there are pokémon that are a bit stronger than even the pseudo-legendaries—slaking, for a noteworthy example—but that’s why there is a list of criteria, rather than just one or two requirements. While, yes, slaking is indeed stronger (offensively, anyway) than all of the pseudo-legendaries under normal circumstances, slakoth are rather easy to find. Thus, they don’t exactly have that mythical element necessary to be considered a pseudo-legendary.

Putting it another way, if legendaries are the gods of a story, then pseudo-legendaries are like the mythical heroes. Just as heroes were designed to be better than ordinary humans due to their cleverness, their strength, and the general uniqueness of their being, the pseudo-legendaries are considered a step above ordinary pokémon for very similar reasons.

It’s not a particularly academic term, I must admit.