Mahmoud, in your example, 'putting out' here means 'giving out' or 'giving forth' or 'illuminating'.

The terms 'put out' and 'put off' have other meanings as well. These are more idiomatic.

'Put out' does mean to extinguish, but it also means to be upset: "I was a bit put out when I found out the concert was cancelled."

And 'put out' means 'to be removed' - "I was put out of the meeting because it was 'members only'.

'Put off' is a similar idiom. "I was put off by him when he started explaining his opinions about not showing up for work." The meaning here is that 'put off' is sort of like taking a mental step backwards from something or someone because you find out that something about that person or situation is unpleasant to you or goes against your beliefs. "He put me off from going to the party when he started talking about the drugs they usually have at their parties."

And lastly, the correct grammar here is:  What is the meaning of "Put out"

You put out a fire or extinguish a fire.

A building caught on fire yesterday but the firefighters got there in a few minutes and put it out.

Put off means to postpone something like a meeting.

There was a blackout and the meeting was put off.

I hope that helps!