Ergative and its counterpart accusative are terms used in linguistics to talk about different kinds of languages. Here's a brief tutorial on the relevant concepts. (Note for linguists: Yes, I'm oversimplifying things and brushing past certain side issues.)
In English and other languages we call accusative, identical case endings are used for subjects of transitive and intransitive sentences, and another set of case endings is used for objects of transitive sentences. So we say "He ate brains" and "He died", but "Cthulhu ate him".
"He" (traditionally called the nominative form)is used for both intransitive subjects (abbreviated S) and agents of transitive sentences (abbreviated A), and "him" (traditionally called the accusative form) is used for patients (those on whom an agent acts) of transitive sentences (abbreviated P). Typically the nominative form is simpler than the accusative form. This can't be illustrated well in English, with its bare remnants of case; but the final -m of him and them is a case ending originally attached to the nominative forms he and they.
But in ergative languages like Basque, S forms are identical with P forms instead of with A forms. So in Basque we'd say (in literal translation) "He ate brains", "Him died", "Cthulhu ate him". The S+P case is called absolutive, the A case is called ergative, and it's the absolutive case that usually has a simpler ending. Most ergative languages are only partly ergative; Hindi, for example, is accusative in some verb tenses and ergative in others.
Now suppose we combine two sentences with "and", like this: "Cthulhu ate him and died". In English that sentence has to mean that it was Cthulhu who died, eh? But in Basque, it could only be interpreted as short for "Cthulhu ate him and him died", meaning that the unnamed eatee (sic) was the one who perished. This is called syntactic ergativity, and not all languages that are ergative in the above (morphological) sense exhibit it.
Chinese, on the other hand, is neither ergative nor accusative. Sentences that literally translate to "Cthulhu dropped the watermelon and burst" and "Cthulhu dropped the watermelon and was embarrassed" are equally valid, and Chinese speakers interpret them according to common sense. That is, "...the watermelon burst" (ergative) and "...Cthulhu was embarrassed" (accusative). Only the latter one reads properly in the English translation because English isn't ergative.
There are languages that use other schemes. Split-S languages use A forms for subjects of some intransitive verbs, and P forms for others. Fluid-S languages can use A forms or S forms as subjects of intransitive verbs depending on context. So "John slept" with an agent case ending on "John" would mean that John chose to sleep, or something like that; "John slept" with a patient case ending would mean it was involuntary. Sometimes it's about whether the S has control rather than volition.These two types are jointly called active languages.
In yet another type, dubbed Monster Raving Loony languages (that name is not official), there is one form for A and P and another form for S! Rushan (not to be confused with Russian) is one of this rare type.
The unusual word eatee that I used above brings up the -ee suffix, which shows just a little hint of ergativity in English. Typically, it makes a P noun out of a verb, like mortgagee, donee, and vendee -- as opposed to -or and -er, which make A nouns out of transitive verbs. But -ee can also be applied to make an S noun out of an intransitive verb, like absentee and escapee. We don't normally talk of absenters or escapers, because -er is ergative, whereas -ee is absolutive. (What to do with bargee 'one who poles a barge', I don't know, and doubt that you do either -- the OED calls it "apparently arbitrary".)