In a language with so many words, this is another which has several different meanings, which seem to be growing away from their origins. I will here concentrate on the one which I find is becoming curious.
The verb wake, meaning to remain awake, to become awake, or (causatively) to rouse from sleep or unconsciousness, actually comes from two distinct but synonymous verbs in Old English, wóc and wacian, which unsurprisingly merged in early English, according to the OED. The former verb has been traced back into Old Norse, the latter into our Germanic roots.
Among those meanings is that of staying watch in vigil over a corpse until burial, although this is now said to be only in dialects and Anglo-Irish usage.
These appear to have become nominalised in Middle English to mean the act of staying awake, again particularly in vigils for the dead, or for a festival, which could be – in country parts – anything but funereal.
Having been applied mainly to mourners keeping vigil over a body prior to its interment, today it is most commonly used for a reception held immediately on completion of the funeral ceremony, usually accompanied by food and drink. Sometimes these wakes get very boisterous, and there is a somewhat irreverent tradition of brawls, punch-ups and other shenanigans occurring at wakes.
I do not know whether this relates to a change in the traditions surrounding death and its observance in English-speaking lands. Wikipedia mentions several different types of wake, including the vigil before burial, viewing of the body either in the home or at a ‘funeral home’ (also known euphemistically as a ‘chapel of rest’), and the gathering after the funeral has been held.
The preburial wake has also given rise to a mis-derivation, which claims that those holding the vigil are waiting in case the corpse should wake up. Although the Victorians in particular were keen to build devices into coffins lest the apparently deceased should be buried alive, that is a misunderstanding.
What is clear is that the modern post-funeral social gathering has become detached from the word’s derivation and original meaning. Anyone struggling to stay awake at a modern wake is likely to have had too much to drink, not to be exhausted by their long and tearful vigil.
Finally, there are a couple of more specialist uses of wake. One, derived from Scandinavian words such as the Old Norse *vaku, describes the ripples or waves left in the water by the passing of a vessel, its wash. Oddly that does not seem to have been recorded in English before about 1600. That is more widely heard in the phrase in the wake of, meaning following, subsequent to. The other use is for a North African bird, and is probably onomatopoeic in origin.