A simplicial set $X$ is said to be fibrant (or Kan complex) if it satisfies the following homotopy extension condition for each $i$:
Let $x_0,\dots,x_{i-1},x_{i+1},\dots,x_n\in X_{n-1}$ be any elements that are matching faces with respect to $i$. Then there exists an element $w\in X_n$ such that $d_jw=x_j$ for $j\neq i$.
What would be the geometric meaning of the definition above? For example for an ordinary simplex?
Thanks for any help.