A contradiction is two propositions used in combination where one makes the other impossible. It is something that is A and non-A at the same time. A contradiction, therefore, cannot exist in reality, since existence exists (whereas a contradiction could not possibly exist). In the cognitive process, reaching a contradiction as a conclusion or evaluation of reality is proof of an error in one's thinking.
A square circle is a contradiction in terms. It cannot even be imagined.
"Anyone who denies the law of non-contradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned." (Avicenna, Medieval Philosopher)