To "have the floor" means that someone has the right to speak at some sort of formal event or gathering. The phrase is an English idiom which has expanded from the original meaning referencing formal meetings to the point where it is used in everyday speech. It can be used whenever a group of people are having a conversation and someone needs the attention of the whole group. As a matter of fact, "have the floor" is often used as a rebuke to anyone who might be interrupting the speech of another person at an inopportune moment.
When someone uses a word or phrase that has a meaning somewhat different than the literal definitions of the words included, that person is using an idiom. Idioms get their meanings not so much from the words themselves but from the way that they are used and understood by the culture in which they originated. They allow for speakers to be colorful and familiar to their listeners at the same time. One idiomatic expression that has grown from formal origins to be used on daily occasions is the phrase "have the floor."
In the setting of a formal meeting, there may be certain circumstances that require a number of different speakers to address the people gathered. Such situations call for some decorum and structure so that the meetings don't devolve into unorganized chaos with many people speaking all at once. The group in charge of meeting usually decides who gets to speak and when, and they are the ones likely to use this phrase. A leader of the meeting might say something like, "We've heard from the two opposing candidates; Senator, you now have the floor."
People became familiar with the use of this phrase in formal settings and thus began to use it more familiarly among acquaintances in their daily lives. It can now be used as a way of saying that someone has the right to speak at any given moment. For example, someone might say, "Now that you've spoken your peace about this topic, allow me to have the floor."
At times, this idiom may be invoked if someone is constantly interrupting the speech of others. When used in this manner, it lets the person doing the interrupting know that this behavior is not to be tolerated. In this context, someone might say, "You've been sticking your comments into this conversation all night long, but now it's my turn to have the floor."