Articulation Point Example

Consider graph: $1-2-3-4$ where edges are $1-2$, $2-3$, $3-4$. Vertex $2$ is an articulation point. Remove it, and you get two components: $\{1\}$ and $\{3, 4\}$. Vertex $3$ is also an articulation point. Remove it, and you get $\{1, 2\}$ and $\{4\}$.

Vertices $1$ and $4$ are not articulation points because they are endpoints. Removing an endpoint with only one edge cannot disconnect other vertices from each other.