Cor is Latin for heart, and tego, tegere means to cover. The bark of a tree, covers the wood.
The AHD definition just doesn't go far enough. Here is from ARTFL Webster 1913 Dictionary:
Cor"tex (k?r"t?ks), n.; pl. Cortices (-t-sz). [L., bark. Cf. Cork.]

1. Bark, as of a tree; hence, an outer covering.

2. (Med.) Bark; rind; specifically, cinchona bark.

3. (Anat.) The outer or superficial part of an organ; as, the cortex or gray exterior substance of the brain.