Those that redstar mentions are coverage ratios, which can be used in two ways: when providing the loan, to size the loan (ie, you do a budget of future cash flows, and say that you want no more than 2/3 of that money to be used to reapy the laon (principal and interest), and you calculate how much debt can be carried that way), or during the loan, to trigger defaults.
It's the second kind that redstar correctly describes as covenants, we also call them coverage ratios. I am not keen defaults based on coverage ratios in my deals, because they are fundamentally pro-cyclical and worsen things at precisely the worst moment. In the long run, we're all dead. John Maynard Keynes
This being said, when the CEO of the company you work for is, today, talking about covenants, she's talking about the coverage ratios. The rest are, especially now that debt and equity markets have largely shrivelled up and investment is way down, less relevant and, in any case, rarely cause an involuntary default. It's this latter thing corporate masters are most fearing today.
And, as Jérôme says, financial ratio covenants tend to be highly cyclical, and so, in the case of the US and the UK, we see highly cyclical monetary and fiscal policy accentuated by private market behavior.
And not enough stimulus, and the wrong kind.
Things are goign to get ugly over here, that's what my gut is saying. Fai de bèn a Bertrand, te lou rendra en cagant