This phrase was all the rage 10 years ago.
The banks had lent money that the borrowers could not pay back, if they foreclosed on all the bad loans, the banks themselves would go bust. So they extended the loans, accepted lower payments and generally waited where they could for companies to come back to health and be able to pay back their debts.
In the round it worked, of course RBS and others also took plenty to the cleaners to help them 'stay afloat', but many of the larger loans and groups were spared. As an example, the housebuilders were in real trouble. Taylor Wimpey's share price went as low as 5p! But the banks knew if they disrupted the house builders then the knock on to the rest of the industry would be unimaginable. Taylor Wimpey had its loans rolled over and recovered fully (in a sense, Wimpey was never in danger, its sales fell a bit, the issue was the lack of credit, not its business model or operations). This was a signal for the banks to 'extend and pretend' that whole sector.
Of course, over time the loans that could not be paid were called in, but we ended up for many years with a zombie economy of companies who could not pay their debts nor die off. This was a sub-optimal outcome, exacerbated by the over use of quantitative easing.
In other countries, things have gone less well. Deutsche Bank still has stuck to extending all loans and not clearing up its loan book, even today, 11 years after the crisis, the bank is a mess and the German Government is trying to figure out ways to get it to merge or other ways to keep it going. There are regular management changes as no one can figure out how to cure the illness with out killing the patient.
The above story has a alternate explanation for not postponing article 50 in the current UK Brexit mess. Postponing Article 50 is the political equivalent of Extend and Pretend, but the UK is Deutsche Bank not the UK or US banks. Extending won't fix anything at all, but continue to paralysis and stasis of the situation today. Whatever the idiots in Parliament decide to do, they need to make a decision as can-kicking now is the worst answer of all of them.