Just that if you have a quantum system, such as a qubit consisting of the |0> state and |1> state with a combination over the two (called a superposition) represented by a|0> + b|1> then a and b can be complex. This is in contrast to classical mechanics where, for example, pr(heads) and pr(tails) must both be real.

It's only once it comes to actually making a measurement that you need to get real again.