What are the effects of liquidity crisis? What are the actual effects of the lack of liquidity?
Economists always say, we need to increase liquidity at a time of recession, but why is liquidity is important for us? Could anyone explain it in an example?
Lack of liquidity depresses the output and can lead to recessions because it forces otherwise healthy firms to go bankrupt and it also undermines the financial infrastructure of an economy. 

I think good way of understanding the problem is to explore the difference between illiquidity and insolvency. When firms go bust it is often mainly due to one of the two following reasons:


Firm is insolvent - when firm is insolvent it means that it is economically not viable. The insolvency means that the firm simply does not generate enough revenue and consequently also profit to meet its obligations.
Firm is illiquid  - when firm is illiquid it generates enough profit to meet its obligations but not enough cash. This is because the customers of the firm might not pay for the products on time (which during the crisis often happens - for example in the current corona virus crisis some people might pay their rents late - some countries even consider canceling them/postponing them). But this the hurts the ability of that firm to pay its employees suppliers and creditors in general. Consequently even though firms business might be economically healthy there might not be able to generate enough cash in short term to pay its own creditors.


(Note: I am using the words insolvent and illiquid in broad economic sense - in finance and accounting those words have little bit more narrow definitions)

You want to let insolvent firms to fail and be replaced with more efficient firms - its the part of Schumpeterian creative destruction. However, firms with liquidity problems are fundamentally healthy- especially when the iliquidity is caused by shock and is not chronic. Hence when illiquid firms fail it is more or less pointless loss. Unfortunately, in practice it is hard to distinguish which firm is actually insolvent and which illiquid and hence it is not possible to just have some regulation that would effectively shield illiquid firms from the bankruptcy (such regulations exists but unfortunately they often turn determining whether firm is insolvent or illiquid into legal battle that has less to do with economics). As a result most economists stress preventing liquidity crises in the first place.

Furthermore, in the above I was talking just about firms in general but liquidity is actually extremely important to the financial sector. Banks assets are essentially illiquid because they offer loans, and they cant just ask the people they lent money to repay it back before maturity. However, banks liabilities are liquid because they consist mostly of deposit accounts from which people can withdraw cash any time they want. Now most countries have deposit insurance - a regulation that helps prevent people frantically withdrawing cash due to fear of bank going bust (i.e. bank runs). However, this does not extent to other financial institutions and shadow banks which can experience runs by creditors who worry that they wont get their money back, and since financial sector is all interconnected falling of these institutions can spread to all other financial institutions. 

Any problem affecting financial institutions will eventually hurt the real economy because financial intermediaries have first order impact on the economy, because many businesses relay on them for financing - especially startups, but they are important overall (see Levine, 2005 for discussion of that). 

So to sum up a liquidity crisis often leads to recession and has negative impacts on economy because it damages the financial infrastructure and forces otherwise healthy businesses to go bankrupt.