A second order desire is a desire about a desire. A first order desire is a desire for something other than a desire.

Example: The unwilling pedophile:

Suppose P finds in himself a desire (want, inclination) to molest young children. Suppose P also wishes (desires) that he (or she) not have that desire to molest young children.

The desire to molest young children is a first-order desire.

The desire to be rid of the desire to molest young children is a second-order desire.

Example: The Dissatisfied Asexual

Suppose A, a 19-year-old male, has no desire to have sex with anyone. He believes that other males his age do have sexual desires. He wishes he too had sexual desires. This desire, to have a desire for sex, is a second-order desire.