means The state of being unable to pay your debts when they come due, because what you owe outweighs what you have or can raise.

from From Latin solvere, 'to loosen, release, pay,' the same root that gives us 'solve' and 'solution' — to settle a debt was to dissolve the obligation binding you. Stick the negating prefix in- on the front and you get the opposite: bound, unable to loosen the knot. So an insolvent person is, quite literally, someone who can't un-tie themselves from what they owe. The word entered English from Latin by way of legal Latin in the 16th–17th centuries, where it has lived among courts and ledgers ever since.