I understand by this passion the union of desire, friendship, and tenderness, which is inflamed by a single female, which prefers her to the rest of her sex, and which seeks her possession as the supreme or the sole happiness of our being.

This quote is talking about being passionately in love with someone. The love includes a strong desire to be with the person, a strong friendship with them, and a tenderness shared between the two people. This love is special and directed toward one particular person and that person is seen as the most important and only source of happiness.