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.