In traditional Catholic parlance, “affectivity” refers to the passions (in modern parlance: generally feelings or emotions) of love that one person might experience for another. It is roughly a synonym for the modern term “affection.”
We can see this usage, for example, in St. Thomas Aquinas’ Summa theologiae, I-IIae, q. 22, a. 2, sed contra:
Sed contra est quod Augustinus dicit, in IX de Civ. Dei, quod motus animi, quos Graeci pathe, nostri autem quidam, sicut Cicero, perturbationes, quidam affectiones vel affectus, quidam vero, sicut in Graeco habetur, expressius passiones vocant.
On the contrary, there is what Augustine said, in Book 9 of the City of God, that the movements of the soul, which the Greeks call pathe, some of our writers, such as Cicero, call disturbances; some call affections or emotions; whereas others, more accurately call them passions, as the Greeks would have it (my translation).
Affectivity includes the feelings that lovers have for one another, but also, for example, the feelings of children for their parents and parents for children, and so on.
The Catechism’s point is that there is no way to form a healthy emotional relationship based on same-sex attraction. Obviously, people who have same-sex attraction can have healthy friendships, but the friendships (and the emotions involved) would not be based on same-sex attraction as such (in particular, not in the way that the emotional relationship formed in marriage is based on the attraction to the opposite sex).
