What is meant by an element n is square in the finite field Fp.
What is the context? How is the fact that it is square used?
It could mean `$\displaystyle x=y^2$ for some $\displaystyle y \in \mathbb{F}_p$'. This `halves' the underlying multiplicative group (the underlying group is cyclic of even order, and so with a bit of work you can see that precisely half of your non-zero elements are squares).