What's the difference between a figure, a number and a digit?

A dictionary says:

Figure: a symbol for a number

Digit: a word, letter, symbol, or figure representing a number.

Number: a mathematical unit used to count or express an amount, quantity.

I don't see a big difference between a figure and a digit. What is it?

You're using a select subset of many definitions for figure, number, and digit.

A digit is a single numeral (0-9), like the digit 5 in the number 5, or the digit 5 in the number 2507.

A number can have one or more digits, like 7 or 2507 or 2,507.38.

A figure can be a shape, a diagram, or a number; if used to describe a number, it can be composed of a single digit or of multiple digits.

• "2507" is a single numerical value but not a digit. Commented Nov 5, 2020 at 14:18

A figure is something that is drawn, which might be digit.

A figure can also be a number or amount, for example in this dialogue:

We will need to pay them off.
What figure do you have in mind?
I suggest 10,000 should be enough.

A digit is a single number in the range 0 to 9. It is the same word for fingers/thumbs and toes, of which we have 10 each.

Sometimes digit and figure can be used interchangeably.

10,000 is a five figure sum.

In computer parlance, each of those figures is referred to as a digit.

A number is an arithmetical quantity, which is written using digits and other symbols, such as a sign and a decimal point.

TL;DR: If you take pictures of yourself, then the number is you, whereas the figures/digits are the pictures.

It is related to the difference between a number and the representation of a number.

A number is a quantity, it is an abstract mathematical entity. It can be represented by many ways. For instance, the quantity of water molecules in a pond may be written 45,584,123,589, or x for an arbitrary constant in an equation, or a distance or graduations on a ruler.

Digits, figures and numerals, as of their primary definition, are related to the representation of numbers. Roman numerals are I, V, X, C, D, M. Modern western numerals ("arabic" numerals) are 0, 1, 2, …, 9. They are text symbols for representing numbers. XIV and 14 are different representations of the same number. Digits (latin for "fingers") are specifically the ten symbols 0, 1, 2, …, 9.

However, as a secondary definition, figure is a synonym for numbers, and digits is a synonym for the numbers 0 to 9. This is a common figure of speech named a metonymy. It is also used in other languages such as French (figures = chiffres, numbers = nombres). Example: instead of writing "the latest numbers (statistics) from Mediametrics were released this Wednesday", people often write "the latest figures".