edited a bit on the wiki in the glossary.
Sacrifice - Place card(s) in discard pile for the purpose printed to use up available resources. When you see Sacrifice at the top of a card, it affects the cost of that card. When you see Sacrifice in effects or abilities area of a card, it affects the effects or abilities of that card. This is a total number of resources, not resource cards.
when looking at prisoner enlistment on egyptian empire, i noticed that it takes three water to capture an opponents soldier from the battlefield. when sacrificing, you are actually discarding these resources. so if you were using the caspian sea (huns) or the lower nile, you could just throw that card away to cover the cost of this sacrifice.
if you didn't have a 1/3 resource but had a couple of 1/2-1/2 resources (tura or memphis), you may have to throw away two cards for a total of 4 to cover the cost of that sacrifice.