Limbo is/was a construction of the early Roman Catholic church as a way to explain what became of those children that died before being baptized, as they were too young to have committed any personal sins. The prevailing consensus then was that, despite not committing any sins per say, the babies would still have to go to hell because they, like everybody else, still had their part in the original sin. Moreover, heaven cannot bear those not of the Christan faith, which the babies technically were not.
Over time, Limbo and Purgatory morphed-colloquially-into the same place. Going by Dante's Divine Comedy, Limbo/Purgatory was geographically the place in hell that was closest to heaven. It was apparently populated by those who had lived a virtuous life, but had failed to convert to Christianity either out of choice or ignorance. Unlike all other levels of hell, Limbo/Purgatory was without active punishment or damnation. It was simply a plane of existence for those who neither met the requirements to ascend to heaven, nor descend to hell. The only possible danger to be incurred by the people of purgatory was to attempt to climb out of it, and towards heaven. That task was apparently impossibly difficult and painful.
And that brings us to the topic at hand, the game Limbo. Per the developers, their only hint towards the story's depth is that the boy we control is on a journey to find his sister. The start of the game has the boy waking up in a forest, staring up at the sky. Later, he crosses a body of water (presumably the river Styx, thereby signifying that the boy is, in fact, dead) and encounters many trials and tribulations therein. It is worth noting that the sister that the boy searches for is seen twice in the game, once at the ending and once at the approximate midpoint. In both cases the girl is surrounded by a light from above, is kneeling, has her back turned towards you, and faces downward mulling the soil, and/or in prayer.
The game ends much the same way it began. As you progress though the game, the settings change from the forest to increasingly sterile and industrial venues. The final puzzle rests in some sort of factory, and results in the boy breaking though a wall. This results in the boy being throw into a forest setting, yet again, and again waking up on his back in a congruent manner as in the beginning. Walking rightward, the boy finds his sister, still kneeling down and turned away, with a rope ladder next to her that is clearly hung too high up for either of them to reach. The latter leads to what appears to be a tree house. The girl makes a startled movement and stands up as the boy approaches, but she never turns around. The game ends here, and the credits start.
If you watch the credits to their end, you are taken back to the title screen, but it has been altered. The background area is now that of the final scene, but different. The rope ladder in the corner now appears torn and broken. All the while the place were the brother and sister once stood is covered in black lumps, which are engulfed in many buzzing flies. The implications are neither obvious nor vague.
Both the boy are girl are dead, as they both persist in Limbo. What you see below the tree house are their bodies, likely a cut away to reality. How exactly they may have died isn't stated, but considering the reoccurring motif of the boy waking up face up the the woods, and the broken latter, he and his sister likely fell out to the tree by accident and died. Considering what has already been said about the history of limbo/purgatory, the two of them were probably unbaptized children. The rope latter then represents the tool of their mutual demise in life, but too does it symbolize their position in the afterlife. They are unable to climb the latter, and as such unable to leave. They are both relegated to Limbo for eternity therein.
A simple and fun story, and unlike a similar game called "Braid" the game-play and plot actually work in unison. As far as this game's appropriate place in the curriculum is concerned, the study of what it is to be a "monster" is a wonderfully broad subject. But that's a subject for another time, just believe me when I say that Limbo works well enough.