Demisexuality does not refer to the active restraint or repression of sexual desires or actions.
Demi- is a prefix meaning half. This is used to mean halfway between sexual and asexual. The term originated in the asexual community, specifically within the Asexual Visibility and Education Network (AVEN).
Demisexual partner: I'd have to reach a higher level of emotional intimacy before I could feel the same way. =\
Sexual partner: Oh, I see. Well, we can do something enjoyable together. =/
Demisexual partner: =D We can bake a cake for now!
Sexual partner: Sure! That's always fun, although we seem to be doing that a lot. =D
Demisexual partner: *squeee! bonding time!*
Primarily, the human will not be attracted to another human, but after being with another human romantically, feelings may begin to develop. This is further elaborated upon by Rabger's Model, which suggest human sexuality is created by four factors: Primary/Secondary Sexual attraction and Primary/Secondary Sexual desire.
Demisexuality is (apparently) a form of asexuality, related to gray-a.
Person 2: My IQ just dropped 20 points listening to you.