What is the meaning of ε?

Emittance.

Extinction coefficient. (Can we add an example for this sense?)

An arbitrarily small number, usually in the company of δ.

The empty string.

Machine epsilon.

The 8th letter of the Arvanitic Albanian Greek-script alphabet.

Lower case epsilon, the fifth letter of the ancient and modern Greek alphabets. Its name was εἶ, later ἒ ψιλόν, and presently έψιλον. It represents roughly the same sound in both alphabets: in Modern Greek, a somewhat lowered variant of the mid front unrounded vowel: /e/ or /e̞/. It is preceded by δ and followed in the archaic alphabet by ϝ and in the classical alphabet by ζ.

hey, oi (said to get someone's attention)

eh, huh (used as a tag question, emphasising what goes before or to request that the listener express an opinion about what has been said)

eh, huh, what, pardon (in isolation, request for repetition or clarification of what has just been said)

I wish, if only (expressing a wish or hope)

oh, just (to precede an offhand or annoyed remark)

oh (expression of wonder, amazement, or awe)

um, er (implying hesitation)

Lower case epsilon, the fifth letter of the modern Greek alphabets. Its name is presently έψιλον. It represents, in Modern Greek, a somewhat lowered variant of the mid front unrounded vowel: /e/ or /e̞/. It is preceded by δ and followed by ζ.

Source: wiktionary.org