1. In the asexual
community, the equivalent of a "crush", but explicitly lacking an interest in forming a romantic couple or having a sexual relationship with the person in question. It does not matter if they are "in a relationship", as long as you two can have a deep connection. A squish is an intense feeling of attraction, liking, appreciation, admiration for a person you urgently want to get to know better and become close with. It is different from "just wanting to be friends" in that there is an intensity about it and a disproportionate sense of elation when they like and appreciate you back.
2. Such a person can be referred to as your "squish".
3. It can be used as a verb, "to squish on someone".
A: So are you... dating right now?
B: No, I'm not looking.
A: (thinks: oh good, that means she will date me)
B: No I really want you to hear what I'm saying: I'm not looking to be in a relationship. But I have two squishes right now.
A: You what?
B: Squishes. They're people I just really love and want to be close to and intimate with - but not in a sexual way. I just feel very connected with them and attracted to them and I want to be important in their lives. But I don't want to be in a romantic relationship with them.
A: Huh? You're weird.