What it does
Gershayim is the doubled form of Geresh. It performs the same light-disjunctive function but with slightly more weight and a different melody. Unlike Geresh, Gershayim does not need a Kadma to precede it.
Where it appears
Less frequent than Geresh. Used in place of Geresh when the word that would carry the disjunctive is positioned without a preceding Kadma, so the trope itself carries the full melody.
How to remember it
Gershayim literally means "two Gereshes." The Hebrew suffix -ayim is the dual form. Visually the mark is two adjacent diagonal slashes above the letter, doubling the single slash of Geresh.
Example from the Torah
Bereishis 1:11
When you see Gershayim, there is no Kadma earlier in the phrase: the trope is standing alone where a Kadma + Geresh pair would otherwise have done the job.
Hear the melody
A synthesized rendering of the melodic shape, not a vocal recording. For a baal koreh's voice on a full aliyah, PocketTorah is a great free resource.
Hand signal (simanim)
Often confused with
Geresh is one slash and needs a Kadma in front of it. Gershayim is two slashes and stands alone. Functionally equivalent in role.