In plain English, absolute value is just a certain distance from 0. Since distance is always a positive value (e.g., you would not say you went -6 feet if you moonwalked to get to a door 6 feet away), absolute value must also be a positive value.
In your example, -3 is 3 units away from 0, so |-3| is 3. Likewise, multiplying a negative number by a negative number yields a positive product, and -3 * -1 = 3... which happens to be the same distance from 0 that we had gotten before. Thus, |-3| = (-3)(-1).
What Jim said was correct. For the person who might not appreciate the absolute value graph, however, perhaps the moonwalking illustration will suffice to get the concept to stick. (I will spare you a video answer.)
Good luck with your studies.