Double-struck capital N

It denotes the set of natural numbers.

In a statement such as n ∈ ℕ, it says that n belongs to the set of counting numbers. It names a set, not one particular number.

Definitions differ on where counting starts: {1, 2, 3, …} excludes zero, while {0, 1, 2, 3, …} includes it. If the definition is missing, the glyph alone cannot settle the question.

Where did this notation come from?

The plain N was used for natural numbers before it got a double-struck style. Richard Dedekind used N for the natural numbers in 1888, and Giuseppe Peano used N for positive integers in 1895, with separate notation for natural numbers including zero.

The double-struck style came later from mathematical writing and typewriting. On blackboards, writers doubled strokes to distinguish number-set symbols; typists imitated bold letters by striking them twice, a practice recorded in the late 1950s and 1960s. The same style is used for ℤ, ℚ, ℝ, and ℂ.