Exodus 16:16 ("Let every one gather of it as much as is enough to eat; a gomor for every man, according to the number of your souls that dwell in a tent, so shall you take of it"); 16:17 ("And the children of Israel did so: and they gathered, one more, another less"); 16:18 ("And they measured by the measure of a gomor: neither had he more that had gathered more; nor did he find less that had provided less: but every one had gathered, according to what they were able to eat").
The g in עמר gomer (the second vowel is short e, not o) is an artifact of the fact that the Greeks could not pronounce the glottal stop ע `ayin letter, so they used the same letter of the Phoenician alphabet for their gamma. (Hebrew script `ayin looks like Greek gamma.). So we have the Gaza strip, Sodom and Gomorrah; in fact, the `Aza strip, Sdom and `Amorah.
An `omer is a solid measure of volume, typically for produce. It is 1/10 of an ephah, and is about 2 quarts.
(Note contributed by Raphael Finkel)