What the sigma symbol means
Sigma (Σ, small σ) is the 18th letter of the Greek alphabet. The capital Σ means "sum": Σxᵢ adds up every x value, and with limits written below and above it, it becomes a full summation from i = 1 to n.
Small σ is the standard deviation of a population, and σ² is the variance, so it appears in every statistics course next to the mean symbol. Six Sigma, a quality-management method, takes its name from it and aims for no more than 3.4 defects per million opportunities. See the standard deviation symbol page for s, σ and related signs.
Science uses σ for the Stefan–Boltzmann constant, electrical conductivity and cross-sections, and chemists call a single bond between two atoms a sigma (σ) bond. Online, "sigma" is also slang for a self-reliant lone-wolf type, which is why Σ turns up in gaming names and memes.
Σ, ∑, σ and ς: four different characters
Σ (U+03A3) is the Greek capital letter. ∑ (U+2211) is the math summation operator; it looks the same in most fonts but is meant for formulas, and it is what a Mac types with Option + W.
Greek has two small sigmas. σ is used at the start or in the middle of a word and ς only at the end, as in κόσμος (cosmos). For statistics you want σ, not ς. The C-shaped ϲ is the lunate sigma found in older Greek writing and on icons, and Ʃ is the Latin letter esh, which looks like Σ but comes from the phonetic alphabet.
How to type sigma
On Windows, hold Alt and type 228 for Σ or 229 for σ on the number pad. On a Mac, Option + W types ∑; for σ, use the Greek keyboard (the S key) or the Character Viewer (Control + Command + Space).
In Word, insert an equation and type \sum for a summation with limits, or type 03A3 and press Alt + X. In Excel, the AutoSum button is marked with Σ. In LaTeX, use \Sigma, \sigma, \varsigma and \sum; in HTML, Σ, σ and ς.