Actually, the modulus of a number x, witten as |x| can be loosely defined as it's length. So for a real number, it is defined as:
|x| = x if x > 0
|x| = -x if x < 0
so |5| = 5 and |-3| = 3
For complex numbers, the situation is more, erm, complex. The modulus is the distance between the origin and the point in the complex plane that represents that number. This can be written as:
|z| = sqrt(x2 + y2)
where z = x+iy (think pythagoras and that'll make sense). So |1+i| = 1.141.... and |-3-4i| = 5
The modulus, and the fact it is always positive is very important in many proofs in analysis. In fact, the whole of complex analysis, and in turn much of the study of calculus, is based in one way or another around this concept.