Heidegger says that Befindlichkeit refers to what is ordinarily called "being in a mood," and also what is called "feeling" and "affect." But Heidegger offers a radically different way of thinking about this ordinary experience. Befindlichkeit refers to the kind of beings that humans are, that aspect of these beings which makes for them having moods, feelings, or affects.
But Heidegger thinks about this human being in a very different way than most people do, and so he also thinks about mood and feeling very differently.
Let me give a rough initial impression of Heidegger's very different basic conception, Befindlichkeit.
In German a common way of asking "How are your is "Wie befinden Sie sich?" This literally says "How do you find yourself?" One can also say to a sick person "Wie ist Ihr Befinden?" ("How do you feel?") The same form can also be used to say that something or someone is situated somewhere, or in some way. For example, one can say, "The White House finds itself in Washington, D.C.," or "I find myself in Chicago," or "I find myself in happy circumstances."
"Sich befinden" (finding oneself) thus has three allusions: The reflexivity of finding oneself; feeling; and being situated. All three are caught in the ordinary phrase, "How are you?" That refers to how you feel but also to how things are going for you and what sort of situation you find yourself in. To answer the question you must find yourself, find how you already are. And when you do, you find yourself amidst the circumstances of your living.
Heidegger coined a clumsy noun from the German colloquial forms. To translate it, let us not look for an existing noun in English, since he found none in German. His noun is like "how-are-you-ness" or perhaps "self-finding."
The reason for being careful about these allusions, and for keeping his sense of the word, is because Befindlichkeit is a new conception and cannot be rendered in old ones.