a nonterminal symbol

If terminals are the finished bricks in the wall, the nonterminals are the labels on the blueprint — 'put a window here', 'put a wall section there'. A nonterminal is a placeholder that stands for a WHOLE category of sub-structure still to be filled in, not for any one final symbol. Building a string means repeatedly expanding these labels until none are left.

Formally, the nonterminals are exactly the variables V of a context-free grammar (V, Σ, R, S). Each one appears on the left-hand side of one or more production rules that say how it may be expanded, and it can also appear on right-hand sides (including inside its own rules, which is how recursion happens). A nonterminal is never part of a finished string; the derivation is not done until every nonterminal has been rewritten away into terminals. It is useful to read each nonterminal as a meaningful syntactic category: in a grammar for a language you might have variables named Expr, Term, Statement, Block — each generating the set of all well-formed expressions, terms, statements, or blocks.

By convention nonterminals are written as capital letters (or angle-bracketed names like <expr> in BNF), to set them apart from terminals. The start symbol is just the one distinguished nonterminal you begin every derivation from. Designing a grammar is largely the art of choosing the right nonterminals: each should capture one coherent kind of sub-phrase, and recursion among them is what lets a finite set of rules describe an infinite, nested language.