Fair use is the idea that it should be okay for a person to reuse something that another person has created, in certain amounts and for certain purposes, without breaking the law.
In most countries, art and other made-up things, like stories, books, TV shows, and pictures, are owned by the person that first made them. This person can let someone else own the things they make, sometimes for money. The person that owns these things has a copyright for them, which means that person can decide who can copy their work. If someone else copies that work without asking the owner first, that person is breaking the law. The owner can take the person to court and try to get money from them because of what they did.
Since a lot of creative work is popular, people want to talk about them, and they may want to talk about them on TV or in a book. This might mean that they want to use a little bit of it when they talk about it. The idea of "fair use" was added to most copyright laws to make sure that it would be OK do to this, as long as only a little bit of someone's work is used.
Since a lot of creative work is now on computers and on the Internet, it is very easy to copy things and send them to lots of people. To make sure that people cannot always do this, there are computer programs that try to stop people from copying other people's work (known as digital rights management). One problem with these programs is that they also mean that you cannot copy even a small part of someone's work, so you cannot do "fair use" without cheating the program. In some countries, cheating those software programs is also breaking the law.