If you are just starting philosophy, good for you. However, you have picked a pretty tall mountain for your first climb. I must confess that I have never read Being and Nothingness, but I can say a little about the term being, which does take some getting used to.
Sartre was influenced by (or, some would say misinterpreted) Heidegger, who is often credited with returning modern philosophy to the "question of being." Heidegger claims that the Greeks were the first to have a distinct term for "being" and were thus enabled to think about the distinction between some "thing" and the "existence of" that thing. In some sense we might say that "being" or "existing" is that which all things have in common, even dreams, fairies, words, trees, people, and theories. They may have very different modes of existing, but we might say all... exist.
But what does this mean? The first thing is to notice that, as with much philosophy, it brings into view something we take for granted, something that becomes invisible to us. Part of Heidegger's argument was that the Greek origins of philosophy lie in this very "not taking for granted" this state of just... existing. Or, as he put it "being there" or Dasein.
One way to get a feel for it is just to look at the words for being. Something exits, is, will be, was, might be, cannot be. Is it the same as saying something is real, actual? When we say an apple is fruit and an apple is red...are we saying it is "identical to" fruit or "equal to" fruit? Just think about the words and let their oddity sink in.
When Heidegger "returned" to being, what he meant was that he reopened "ontology," the study of "what things actually exist." That is one of the main branches of classical philosophy, along with logic, ethics, and "epistemology," or how we come to "attain and verify knowledge." Since Kant, philosophy had moved away from "useless arguments" about ontology to focus on epistemology or "how we know" what we know. Heidegger and his lineage, including Sartre, turned back to the close observation of being, or in what manner things around us exist. What organizes those things? Are we just an empty center of "beings" or "existences" encompassing our own... being?
This is not an explanation, obviously, but I hope it gives you a feel for the approach. I would encourage you to look at some guide books, philosophical dictionaries, and other references on "ontology" and "existentialism." Sartre's "formal" work is dense and difficult. A massive French misinterpretation of Heidegger written on amphetamines, some might say. It builds on a very complex set of issues and terminologies that pass from Descartes through Kant, Husserl, and Heidegger. So it is hardly surprising one doesn't just "get it."
One final tip. Always look at the etymology. Take the words "being" or "is" or the French or Greek, or any other apparently common words you encounter in philosophy, and just look back at the history of the word's parts and meanings. We take words for granted, and in philosophy you have to "freeze" them, put them in a specimen jar, and examine them carefully, noting how odd they really are.
