You are insolvent if your owe more than you own. For example, if your only asset is a car worth £1,500 and you owe £15,000, you could be considered insolvent.
If you cannot pay your debts, you are also insolvent. Anyone who can only afford the minimum payments on their credit cards is likely to be insolvent. Importantly, this is also likely to mean that their debts will be growing each month, with no likelihood of being able to repay the balances in full.