In a state of being neglected and immobile, with no prospect of movement to a better place.
For those of a certain age, limbo is now most often associated with the party dance, in which dancers bend backwards and shuffle under a horizontal stick without touching it. This originated in the West Indies the 1950s and became something of a fad in the 1960s. The craze was created, or the uncharitable might say, cashed in on, by Chubby Checker, who released the single Limbo Rock and the album Limbo Party in 1962. The adjective 'limber' has been in use in English since the 16th century, with the meaning 'pliant and supple; easily bent'. There's no definitive documented link between limber and limbo, but it seems very probable that they are actually versions of the same word.
People had been in limbo well before the 1950s, of course. Limbo was originally a place rather than a dance - the borders of Hell, no less. That limbo derived from the Latin 'limbus', meaning edge. Mediaeval Christian belief had it that only those who were baptized into the Christian Church could enter Heaven. Theologists, especially those of the Roman Catholic persuasion, were much exercised by the fate of those who, while not being sinners to be condemned to Hell, were unbaptized through no fault of their own. In particular, babies who died at birth or those who had died before the time of Christ, would have had no choice but to remain unbaptized. By the 14th century, the incongruity was avoided via the concept of Limbo, the abode of righteous souls who weren't destined for either Heaven or Hell. Two of the forms of Limbo were Limbo Infantum (Limbo of the Infants) and Limbo Patrum (Limbo of the Adults).
Thus, Limbo was on the border, not in Hell, but not in Heaven either, and 'in limbo' later came to take on the metaphorical meaning - 'in prison'. Shakespeare used this in Henry VIII, 1613:
I have some of 'em in Limbo Patrum, and there they are like to dance these three days.
Soon after that, the meaning was extended to our current usage, which refers to any situation where someone or some project is confined and neglected, with nowhere to go until something happens to restart it. This was alluded to in John Milton's An Apology..., 1642, in which he refuted an attack that had been made on a Presbyterian group known as Smectymnuus:
"I am met with a whole ging of words and phrases not mine, for he hath maimed them and ... mangled them in this his wicked limbo."
Mediaeval belief had it that the spirits of those in limbo were all around us (and many still believe this). These days, Limbo remains close by. 'In limbo' is the name that computer scientists give to the condition of files which are deleted from view but not yet physically removed from storage - like those in the Windows' Recycle Bin.