The common term "being" simply conveys presence. Something "is".

Heidegger saw living as a human being as fundamentally not inert, not just sitting there existing, but as something else. To us, life is an immersion of consciousness in a world which presents possibilites of action to us. So being to us is what he would call being-in-the-world. There is no being-there which is not a relation of agenthood to world.

ELI5: When we say someone "is", we're usually just mean they're physically there. Heidegger's being addresses what they can do in the world they're in.

Edit: I'd like to clarify that I think, as mentioned below, Heidegger wanted to emphasize that a thing's notion of being ought to include the world (the setting) it exists within. I was writing from the perspective of what dasein's being is, which is an agent which, unlike the chair, whose "chairhood" is inert, waiting to be acted upon, dasein's being is one which acts in that world. I'd love any further clarifications or corrections that can be made.