Being 'laid off' is different to being 'fired'. Both mean you lose your job but they are different. 

If you are fired it means you have done something wrong that causes the company to terminate your employment permanently. You may have broken the  company's rules or policies, or your personal performance is unsatisfactory and you are not meeting targets. The company will then sever your contract and 'fire' or 'sack' you.

I think Krish's explanation was good. Being 'laid off' means the person loses their job, but it usually has nothing to do with their personal performance. The company may be downsizing or have other problems which there isn't any work for them to do at the moment. Layoffs can also be temporary, maybe there will be work in the future and the person gets rehired.

And you can say 'they're going to lay me off'. For example

Person A 'What do you think is going to happen at work tomorrow?' '

Person B 'I'm not feeling good about it, I think they're going to lay me off.'

It means to reduce the number of employees by ending their employment. This usually happens when the company is facing a problem. :)

Paul, Krish and Johua, thank you very much for explanation. 

It means to fire them - to end their employment. It's generally American and personally I feel it's colloquial although I may be wrong.    Examples 'I've been laid off'  or 'I'm going to lay off some workers tomorrow'. I don't think you can say 'they' re  going to lay me off. " 

discharging employee/s