Begging the question is a fallacy in which the proposition or conclusion to an argument is found in one of its premises. Stated another way, it "begs" or assumes a conclusion in ones "question" or premise. Though technically different, I am going to lump circular reasoning in with begging the question.
The form of the argument can simply be: A is true because A is true. An example of this would be "Opium induces sleep because it has a soporific quality". Soporific means causing or tending to cause sleep. Restated this is like saying "Opium induces sleep because it tends to make one sleepy.
It may also take the form of: A is true because of B. B is true because of A (circular reasoning). An example would be: "I once overheard three brothers dividing two candy bars. The oldest one gave each of the two younger ones half of a candy bar, and kept a whole bar for himelf. When asked why he got more candy, he said he was the smartest. A few minutes later, one of the younger ones asked why he was the smartest, and in reply the oldest said 'Because I have more candy.'" Ernest J. Chave, Personality Development in Children (Univ. of Chicago, 1937), 151.
The most common example of circular reasoning is: Tom - "Do you believe in God"? Steve - "I do". Tom - "Why do you believe in God"? Steve - "Because it is written in the Bible that God exists". Tom - "Why do you believe what the bible says"? Steve -"Because it is the word of God".