I was reading and I encountered something that goes: We have degree $d$ polynomials in $s$ variables $F_1, ..., F_n$ with coefficients in integers. Let $X$ be the complete intersection defined by the simultaneous equations $$ F_1(\mathbf{x}) = ... = F_n(\mathbf{x}). $$
I have looked up complete intersection on Wikipedia, but I still quite don't understand exactly what it is. Could someone possibly give me an explanation of what complete intersection is and why the definition is that way? Thanks!