"omg she/he/it's so cute, I just wanna hug it ^^"
No defining term. Cute generally descriptive and acceptable enough reason for this reaction.
Males have societal issues with actually performing the above due to age old stereotypes. Many would never be comfortable reacting like that to "cute".
Moe is thus a replacement of such a term for the anime community.
MOE being descriptive for that which is cute, adorable, huggable, lovable. Mostly non-sexual.
Some men of course, get confused over their analysis of "cute" as being sexually oriented. Much due to societal standards of men not often thinking in terms similar to females until recently.
Not that it's completely unusual to be turned on my "cute/moe", as a lot of it is simply visual appeal and a viable sexual partner may be judged through looks to a large degree, especially in materialistic modern society.