A contradiction is a situation or ideas in opposition to one another. Declaring publicly that you are an environmentalist but never remembering to take out the recycling is an example of a contradiction.
A "contradiction in terms" is a common phrase used to describe a statement that contains opposing ideas. Examples of a contradiction in terms include, "the gentle torturer," "the towering midget," or "a snowy summer's day." A person can also express a contradiction, like the person who professes atheism, yet goes to church every Sunday.