Anatoly Liberman wrote at blog.oup.com on 1.8.12:
“Of all our names of the months, April has the most convoluted history. The Romans called it Aprilis mensis, and it seems natural to suppose that in the adjective Aprilis the name of some deity is hidden, but none of the Roman gods or goddesses provides a good match. Aphrodite has been suggested as a possible candidate. Although the match is far from perfect, we will return to it below. Other suggestions have also been made.
In Ancient Rome, April was the second month of a year and the calendar made some use of ordinal numerals before the word mensis. (Compare quintilis (July) and sextilis (August).) Such colorless names devoid of religious connotations were easy to replace with new ones. Hence the idea that originally the first syllable of Aprilis was ab “from,” a prefix and a preposition with ties in and outside Germanic (of is one of its cognates, as is its late doublet off) and present in numerous English borrowings from Latin and Old French, such as abdicate, abduct, abscond, absolve, and the rest. The Latins allegedly forgot the meaning of aprilis, whereupon folk etymology connected it with aperire “opening” (compare Engl. aperture) and took it for a contraction of aperilis (unrecorded)…
When a Latin word defies all attempts at explaining its origin, it is customary to resort to Etruscan. Unlike the pre-Germanic substrate about which something was said in the post on herring, the Etruscan language has not been completely lost. Several hundred Etruscan words, including a few divine names (theonyms, as they are called in special works), have come down to us and their meaning has been ascertained with a fair degree of confidence. One of such words is allegedly apru, from Greek Aphro– “Aphrodite.” Referring to Apru is the only way to etymologize April as “the month of Venus” (Venus being the Roman counterpart of the Greek goddess). This hypothesis takes a good deal for granted. No other month of the Roman calendar owes its name to Etruscan. So why just April? If at the time of presumed borrowing the Latins understood the meaning of apru (Apru), why didn’t they replace it with Venus? All things considered, the Etruscan origin of April is hardly more convincing than the others we have examined here. None of the tentative suggestions discussed above looks pervasive. The Romans had no clearer idea of the etymology that interests us than we do (a small comfort).
I’ll finish by adding insult to injury. The origin of All Fools’ Day is unknown too and there are as many conjectures about it as about the etymology of April. But it isn’t fortuitous that the festival is held at the vernal equinox, when “the earth opens to receive new fruit(s)” and the world rejoices. This is the time for carnivals, tomfoolery, and relaxation. So let us not take our etymological ignorance too seriously. What else could be expected of the name of such a month?”