According to many dictionaries, erogation comes from the Latin for "the art of giving out or bestowing", but currently seems to be heavily linked to the coffee business. I'd like to know how this happened.
A quick Google search turned up a (slightly broken) page with a blog post about this very topic.
The author was curious about that word in the context of an espresso machine's LED display. The author's hypothesis, which I find quite plausible, is that the word is a mistranslation of the Italian verb erogare, meaning 'to deliver, to supply (water, electricity, gas)'. In the author's words:
"Who makes coffee machines? Italians. What do they speak? Italian..."