Context: insurance, risk management
In insurance, solvency refers to the ability for the insurance company to pay out claims and expenses as they fall due. Because generally the amount and the timing of the claims are not deterministic, great care needs to be taken to ensure that the insurance company has enough money (in insurance-speak, "reserves" or "capital") to meet future payments. Whenever a company does not have enough money to do so, ruin occurs.
Modern governments try very hard to prevent ruin from happening, and thus they have raised the standards for solvency. Generally, the prudential regulator will specify a minimum amount of reserves that an insurance company must have, otherwise the regulator can, in effect, take over the company. These regulations come in various names, such as "solvency requirements" and/or "capital adequacy requirements".