Numeral
A numeral is a symbol or combination of symbols used to represent a number, such as "7," "VII," or "seven."
Definition
A numeral is the written symbol we use to show a number: the number itself is an idea, while the numeral is how we write that idea down. Numeral systems include Hindu-Arabic (our standard $0$-$9$ digits), which is positional, and Roman (I, V, X, L, C, D, M), which is additive/subtractive and non-positional. Formally, a numeral is an expression in a numeral system built from a base $b$, representing $n$ as a finite or infinite string of digits using the polynomial value $\sum d_k \cdot b^k$; the distinction between a number (abstract object) and its numeral (syntactic representation) matters in mathematical logic and computer science.
Example
The numeral "$5$," the Roman numeral "V," and the word "five" all represent the same number, just written differently, and forty-seven can likewise be written as $47$ (Hindu-Arabic), XLVII (Roman), $101111$ (binary), or $2F$ (hexadecimal). In Peano arithmetic, each natural number has a canonical numeral: $0$, $S(0)$, $S(S(0))$, and so on, and the standard numerals $0, 1, 2, \ldots$ are abbreviations of these.
Key Insight
A number is an abstract idea (the concept of five-ness), while a numeral is the symbol we use to write it, so one number can have many different numerals. The positional Hindu-Arabic system, adopted in Europe through Arabic mathematicians, replaced Roman numerals precisely because arithmetic (like long multiplication) is far easier with a positional system. Godel numbering pushes this idea further, assigning a unique numeral to every formula in a formal system so it can "talk about" its own syntax, a technique central to the proof of Godel's incompleteness theorems.