Term for a subset $B$ of poset $A$ such that $\forall b \in B,\forall a\in A: a<b\Rightarrow a\in B$

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Suppose that $A$ is a poset, and $B\subseteq A$ such that:

$$\forall b \in B,\forall a\in A: a<b\Rightarrow a\in B$$

This set has a special name. I studied properties of this set in my class, but we called it in a really weird name. I can’t find the name of the set in English. Can someone tell me what is the name of the set in English?

Thanks.