This confused me at first too. Another way to think about this is visually (I'm a big visual thinker so maybe this will help you as well).
Expanding on zezba's example, let's say we want to draw a quad using two triangles:
As s/he pointed out, this can be done with just four vertices. So your vertex buffer would contain only FOUR entries. I'll label these {A, B, C, D}:
However, since graphics processors deal with triangles, we still need to define groupings of THREE vertices to tell the GPU how to create triangles out of the list of vertices already defined. This is the purpose of the index buffer.
You can think of the index buffer simply as a list of indices INTO the vertex buffer that defines triangles. So since we are forming two triangles, and each triangle needs three vertices, the index buffer will need SIX entries.
Ordering matters a bit here too. I won't go too much into that but let's just say I want to define my triangles counter clockwise. I'll define my two triangles as {B, A, C} and {B, C, D}. It's perfectly fine to reuse vertices for multiple triangles.
So my buffers end up looking like this:
Hope this helps.