It seems like currency in Brazil has been changed many times over the period of its existence. The last time the currency changed was in 1994, with the introduction of the modern Brazilian Real (BRL, R$). Why has Brazil's currency been changed so often?
The present Brazilian Real was introduced in July 1994, by President Itamar Franco. It was part of a broader plan to stabilize the Brazilian economy (the "Plano Real").
A series of economic crises and significant levels of inflation had led to the effective collapse of several variants of Brazilian Cruzeiro, and the Brazilian Cruzado. Essentially, as each currency became worthless it was replaced by the next in the series.
The list provided in the question shows the relative values of the currencies. As it says, one 2016 Brazilian Real is worth about 30 US cents, or approximately 2,750,000,000,000,000,000,000 1942 Brazilian Reals. You have to admit that's a pretty unmanageable number, even with banknotes!
The last line on that wiki page (as of today) I think should be a pretty big clue:
Thus, one modern Brazilian real is equivalent to 2,750,000,000,000,000,000,000 times the old real, that is, 2.75 sextillion réis.
This is since 1942. Over the same period the same calculation on a US dollar says you'd need about 15 of them today.
Obviously a currency where even the smallest bill in circulation has at least three 0's on the end is kind of a pointless unit, just like we don't measure people's weight in milligrams. So whenever the currency achieved that state, a new one was introduced.
Changing the monetary unit and name during economic reforms is a way for government propaganda to signal 'things will be different now, trust us, this time it will work'. One actual semi-official slogan was 'Tem que dar certo!' ('it HAS to work!'), from Plano Cruzado, 1986, which created the cruzado (1 cruzado = 1000 cruzeiros, the former unit).
It is necessary to cut zeros from the numbers, and then you need a different monetary unit. Things get really messy in your head when you are used to counting units and after a couple years you need to pay 1000 'moneys' for bread, when everybody in the middle class is a millionaire and a house costs hundreds of millions. Also, most paper forms and even early computer programs did not have space for so many zeros, it was really funny times... and lots of mistakes when filling checks or any documents.
So, going back to paying 1 monetary unit for a loaf of bread, using a shiny new coin, is a psychological signal that 'things will work out now'.
Brazil suffered from chronic inflation for most of its republican history (1889 forwards), with some cases of hyperinflation (and chronic hyperinflation) during subperiods.
As someone said above, the Brazilian currency of nowadays is equivalent to 1/sextillion of the Brazilian currency of 1942 (in comparison, US dollars are 1/15 equivalent to 1942 US dollars).Most governments when implementing stabilization plans for the currency changed its name.
The reason for this chronic hyperinflation was persistent government budget deficits, which were paid by printing money or government-owned banks giving the government itself credit (which is tantamount to printing money in the grand scheme of things, money in the end is one end of the credit spectrum), mostly Banco do Brasil (which still is a state-owned bank, but can't pay for government expenses anymore). A good source for this if you can read Portuguese is "A ordem do Progresso: cem anos de política econômica republicana, 1889-1989". It was the book I read in college.