What is a debt default? The debt ceiling?

The above video gives a very good description of the debt ceiling. But some might put more emphasis on the current scale of US debt - which has edged up towards $17 trillion at an alarming rate - see debt clock here. 

What brought the debt ceiling back into political play has been growing consensus that the debt is now unsustainable in the long term. What Democrats and Republicans battle over is what to do about this.

It is universally agreed debt default (see below) could have a potentially catastrophic impact on the world economy. This prospect will eventually lead to some sort of deal but the two parties will fight bitterly until the last moment.
What is a debt default?

A failure to meet a legally agreed payment. This usually means that the agreement - for example a mortgage - is no longer valid and the lender can take steps to recover the value of the loan
Why would a US debt default be a disaster?

Usually the national currency falls in value and this helps to make the goods of country concerned more affordable. International institutions like the IMF also arrange repayment plans or write offs/markdowns of debt.

For the US, however, none of the above options are feasible. It is literally too big to fail,