A Tessellation (or Tiling) is when you cover a surface with a pattern of flat shapes so that there are no overlaps or gaps.

A regular tessellation is a pattern made by repeating a regular polygon.
There are only 3 regular tessellations:
Triangles Squares Hexagons

A vertex is just a "corner point". 

What shapes meet here?
Three hexagons meet at this vertex,
and a hexagon has 6 sides.
So this is called a "6.6.6" tessellation.