The phrase "too big to fail" came in to popularity as a description for banks, automobile manufacturers, and other private businesses that were considered as so important to the national and/or world economy that they had to be supported through US government investment.
Entities are considered to be "too big to fail" by those who believe those entities are so central to a macroeconomy that their failure will be disastrous to an economy.
The reasons why some organizations received this classification are many. One important factor is the number of people directly employed by a particular company and by subsidiaries that would be adversely affected if the company went bankrupt. The risk of causing large numbers of people to loose their jobs was a critical consideration in the bailout programs arranged for the Detroit car manufacturers.
Large banks may have investments in businesses and organizations around the world. The failure of a number of banks could have huge ramifications on international trade and economic conditions in other countries.