It's a slightly lower energy state, as previously mentioned, the explanation comes from the quantum mechanics equations. You don't need to know why for the MCAT. Most cases of it actually making a difference have to be found experimentally. You can't just look at most molecules and assume that the special stability makes a difference.
If you get a question asking why an odd configuration happens in a given atom (an 's' electron migrates to a 'p' shell for 3 or 6, or to a 'd' shell for 5 or 10 (Cr is the classic example)), then you have an answer, but it shouldn't normally be used as a 'fill in this atom' question (because you can't definitely tell).
Has to do with the spin states. Half-filled shells all have the same spin and fully-filled shells have same spin pairs. Adds to the stability of the atom.