Limbo is an unofficial term for the location where monsters are located before their Summon is successful (during the Summon negation window).[1]
If a monster's Summon is negated, it is not sent from the field or its original location to the Graveyard. So if the Normal Summon or Flip Summon of "Sangan" is negated, it will not be able to activate its effect because it was sent from 'nowhere' to the Graveyard, not from the field to the Graveyard.
Since the monsters in limbo are not considered to be face-up on the field, if they have a Continuous Effect, it is not applied at the time. So if "Jinzo" would be Normal Summoned, "Solemn Judgment" can be activated to negate the Summon. There are some monsters whose effects state that their Summon cannot be negated, meaning that once the monster leaves its place of origin and enters limbo, its summon cannot be stopped by "Solemn Judgment" in limbo, such as "Holactie the Creator of Light".
When a Gemini monster is Gemini Summoned, it is moved to limbo, but Equip Cards equipped to it are not destroyed and Continuous Effects that _target it will not be disrupted (although it will be unaffected by these during the Summon negation window). If the Gemini Summon is negated, it is not considered to be sent from the field to the Graveyard, or even to have left the field (but Equip Cards equipped to it are destroyed as it is no longer a valid _target). As such, if "Nightmare Wheel" _targets a face-up Gemini monster treated as a Normal Monster which has its Gemini Summon negated, it will remain on the field meaninglessly.
Xyz Materials
With the introduction of Xyz Monsters, limbo has unofficially been used to describe the state in which Xyz Materials exist, as they are neither on the field, nor in the graveyard. Entering limbo from the field does not count as leaving the field. Being sent to the Graveyard from limbo does not count as leaving the field either.
Yu-Gi-Oh! BAM
In the source code of Yu-Gi-Oh! BAM, during battle, along with usual terms found in that game such as "Attack", "Boost", "Immunity", "Death", "Negative Boost" and "Effect Trigger", the term "Limbo State" can also be found.