A Contradiction is something that is Logically impossible, due to two or more attributes of the thing in question that cannot coexist. A contradiction is synonymous with a paradox. For example, circular squares are a contradiction because circles and squares have characteristics that are mutually exclusive. A shape cannot both have and not have four 90* corners and four straight, equal sides at the same time.
The Christian God has several attributes that lead to contradictions. As a result, God cannot exist.