A simplex is a point, line segment, triangle, tetrahedron, or higher-dimensional analog.

A simplicial complex is a bunch of simplices stuck together (adjacent simplices might share a lower-dimensional simplex as a common boundary).

https://en.wikipedia.org/wiki/Simplicial_complex

I’m not convinced “abstract” is a good word here, but what they mean is that it doesn’t have any metrical/geometric relationships beyond the graph structure.