The ability of a financial institution to ultimately repay obligations by a given time period. If a bank is classed as being solvent it means the value of its assets outstrip the value of its liabilities and therefore even if a bank runs into unexpected liquidity problems it has enough value to cover these liabilites to prevent problems and ultimately bankruptancy. Another way of describing this is if the losses that banks make on their assets exceed the level of equity capital they have then they are unable to act as a buffer stock to absorb losses.
Below is a graphic to summarise the definition of this form of protection for a bank.