Bill-lock is a situation in which a nations finds that it's daily bills exceed daily income. This can either be temporary, as in the case of being the recipient of a nuclear missile, from which the nation will recover by itself in one to two weeks, or permanent.
The permanent bill-lock condition is generally suffered by large nations that have lost a significant percentage of their infrastructure due to war (the numbers vary, but around 60-80%) but have retained their wonders, improvements and military arsenals. The bills for these items can be in excess of half a million, per day. Nations with severely reduced infrastructure, particularly in the 1,000-1,150 region may not make enough per day in taxes to pay these bills in addition to their normal infrastructure bill.
As you can't pay bills, you can't (after 3 days) buy any infrastructure, therefore you can't increase your income to a level where you can pay your bills, hence "bill-locked".
The only way out of this situation is either through receiving sufficient aid to pay bills and boost infrastructure levels past the break-even point, or to sell-off improvements, nuclear weapons, cruise missiles etc. until your bills are reduced to such a level that you are able to pay them.
