Why do the electron configurations of chromium and copper seem to disagree with what is expected according to the Aufbau principle?

Some elements do not follow the Aufbau principle, there are some alternate ways that electrons can arrange themselves that give these elements better stability.

Explanation:

Using the Aufbau principle, you would write the following electron configurations

Cr = [Ar] $4 {s}^{2}$ $3 {d}^{4}$
Cu = [Ar] $4 {s}^{2}$ $3 {d}^{9}$

The actual electron configurations are:
Cr = [Ar] $4 {s}^{1}$ $3 {d}^{5}$
Cu = [Ar] $4 {s}^{1}$ $3 {d}^{10}$

To understand why this occurs, it is important to realize that...
1. Completely filled sublevels are more stable than partially filled sublevels.
2. A sublevel which is exactly half filled is more stable than a partially filled sublevel which is not half full.
3. Electrons are lazy and will do whatever places them in the lowest energy state = which is the most stable state

In both examples, an electron moves from the 4s sublevel to produce a 1/2 full 3d (Cr) or completely filled 3d (Cu). This gives the atom greater stability so the change is favorable.
http://ericscerri.blogspot.com/2012/07/anomalous-configuration-of-chromium.html

It is important to note that this explanation is just looking at the examples of Cr and Cu. There are other elements which will have exceptions to the rules we have come up with to predict electron configurations. For example, W will follow the Aubau principle and not display behavior like that of Cr. This is due to the fact that the atoms and electrons know nothing of the rules we (humans) come up with to try to explain and predict their behavior.