“So now I'll open the floor for questions.”
You've just finished giving a 15-minute presentation at an event for people to practice giving speeches in English. Now you want to give the audience a chance to ask you questions, so you say this.
So now I'll open the floor for questions.
You can use this expression to transition between different activities when you're leading a group of people. For example, after a science teacher has finished explaining one topic he can say:
So now let's move on to Chapter 15, "Biodiversity".
If you're presenting a new piece of software at work, you can explain what it does first and then use this phrase when you want to start showing the audience how to use it:
So now I'm going to demonstrate precisely how that works. Take a look at the screen here...
To "open the floor to questions" means to allow people to ask questions in a large meeting, lecture, conference, or other group. This phrase is pretty formal, so you use it at the end of a formal speech.
"The floor" is also used to talk about who has the right to speak in a formal discussion. For example:
Senataor Meeks has the floor.
This means that Senator Meeks is allowed to talk. Other people are not allowed to talk at that time.
Chairman Kline, may I have the floor?
This is how you ask for permission to speak in a very formal discussion, like in a political committee or a company stockholders meeting.