What is normal crossing?

I could not find any reference for normal crossings. The definition here is not so clear to me. In some texts, they sometimes said that two varieties have normal-crossing (non-normal crossing) with singularity .... Could some one tell me what exactly this means? For examples, what does it mean if two varieties $V(f)$ and $V(g)$ where $f,g$ are two polynomials, have normal crossings?

Many thanks in advance.

Solution 1:

Mustata's notes on page 69 give a good definition: math.lsa.umich.edu/~mmustata/lecture_notes_birational.pdf.

Basically if your variety is $n$-dimensional, you want a divisor whose irreducible components are smooth and that intersect each other at any given point like (at most $n$) hyperplanes would intersect each other. For example, in dimension 3, the following picture could locally represent a SNC divisor, where the lines actually represent smooth irreducible divisors:

Edit: This is the definition of a simple normal crossing divisor.