One explanation:
The kind of colonization.
Sociologists and anthropologists talk about two kinds of colonies:
Colony of settlement
Colony of exploitation
In a "colony of settlement", entire families (including women), come from the colonizer country.
In a "colony of exploitation", it's less usual the arrival of families, and it's much more usual the arrival of "adventurers" who are usually single men. The number of women that come from the colonizer country is much smaller than in a colony of settlement. And that large number of single men tend to take native women or slaves as spouses.
Almost all countries in Latin America were colonies of exploitation, unlike the USA and Canada, that were mostly colonies of settlement.
Another:
The variation of racial groupings between nations is at least partially explained by an unstable coupling between historical patterns of colonization and miscegenation. First, divergent patterns of colonization may account for differences in the construction of racial groupings, as evidenced in Latin America, which was colonized primarily by the Spanish. The Spanish colonials had a longer history of tolerance of non-White racial groupings through their interactions with the Moors and North African social groups, as well as a different understanding of the rights of colonized subjects and a different pattern of economic development.
I know Spain is not Portugal but the culture of Portugal and Spain are undeniably more similar than that of England
edit: I'm not an expert in Brazil. I'm Puerto Rican and we're taught in school that like most Latin American countries, our blood is part Native, part Black slaves and part European White which is why we look the way we do. Every country is different in the percentages, however. In Argentina, Uruguay and certain other countries you're more likely to see European looking people. In Mexico and much of Central America you're more likely to see Native looking people. In the Dominican Republic you're more likely to see Black looking people, but every country is mixed to a certain extent. I know it's the same in Brazil, but I'm not a Brazilian historian, so I would love to hear from someone more qualified than me in Brazilian history.
The race mixing actually began before emancipation in Brazil, because the percentage of free blacks there was so high. In 1888, the year that Brazil abolished slavery, around three-quarters of the blacks population was already free due to a high manumission rate. A European visitor in wrote that black Brazilians “seemed to be the most intelligent person [he] met because every occupation, skilled and unskilled, was in the Negroes’ hands…They were… the skilled artisans who built the houses, carved the saints in the churches, constructed the carriages, forged the beautiful ironwork one sees in Brazil, and played in the orchestra.” Because of this, blacks were much more integrated into Brazilian society than in the US, and Brazilian blacks had an easier time marrying white people of similar social standing. In 1844, the United States Magazine and Democratic Review wrote of Latin America in general that "the negro is already a freeman- socially as well as politically, the equal of the white. Nine-tenths of the population there is made up of the colored races; the Generals, the Congressmen, the Presidents are men of mixed blood.”
Essentially, intermarriage with the native population was encouraged in Brazil, or at least more so than in other Latin American countries, and especially the U.S.
Race in Brazil was also more fluid; if you married into a higher social class, your "race" could actually be re-classified, officially. So two people with the same skin color could be considered to be of different races, depending on their families. There were even some cases of people paying to have their racial classifications changed. This was much different than in the U.S. where race was more clear cut.
Also, probably most important, the Brazilian colonies were not made up of families of settlers, so there was more racial mixing in Brazil from the very beginning.
See: The Idea of Race in Latin America, 1870-1940 edited by Richard Graham, and Race and Ethnicity in Latin America by Peter wade
edit: cleaned up post and added the two sources I remember most
Adding to other comments: slavery was only officially abolished in Brazil in 1888, but that was just the end of a long gradual process. Since 1850 there were laws that were already granting freedom to certain groups of black slaves.
The group of people who were in favor of slavery was headed by most of the owners of big monocultural farms, who profited greatly from the cheap slave labor. Throughout the 19th century, other parts of society grew more and more fond of the idea of abolishing slavery altogether. Because of that, landowners elite (who had a huge influence on the government) agreed on some compromise laws which gradually freed more and more slaves, until the complete abolishment was inevitable. The most important of these laws were:
In paper, these laws sounded like an advance, but in practice, they were just a "smoke screen" to curb the abolishers' enthusiasm and buy more time for the landowners who wanted to keep slavery. The 1871 law didn't have any effect, as the children would either have to stay at their parents' owner's farm until they turned 21 or be given to the government. Very few children were sent to government care, mostly sick and blind. The 1885 law was also very limited, as it was quite rare for a slave to stay alive until they turned 60, because of the extremely harsh work conditions.
Of course the abolishers weren't happy with that, and the movement became very strong during the 1880's. There were even raiding parties on farms to free slaves and help them escape and hide. The states of Ceará and Amazonas abolished slavery independently from the Empire in 1884.
So by 1888, when full abolishment finally happened, black people were - to a certain extent - already integrated into society. This acceptance of course helped into a greater race mixing in general population.
I'm wondering whether this also has something to do with the way race is classified in different places? My understanding is that a huge number of people in America who are regarded as either 'black' or 'white' are in fact mixed race. A significant number of Americans who are not recent immigrants are actually some mixture of European, African, and native descent, but legal classifications and efforts to clearly delineate racial groups create an image of greater difference than actually exists. My impression is that many Latin American countries have more fully adopted the notion of 'mixed race'. I could be wrong about this.
The book 'black, white, and Indian' by Claudio Saunt talks about the ways that mixed race people in America were defined as belonging to one race or another. So, 'race mixing' might be more prevalent in Latin America than the US, but it's still maybe way more prevalent in the US than people typically imagine.
I got no source other than Wikipedia, but I'm a descendent of a japanese family, being the third generation of this family in Brazil. (I just happened to be born in Japan, though) I know that the Japanese, around 1908, started to settle in Brazil, mostly São Paulo, to work in the coffee plantations. As many already said, the slavery had been long abolished, creating a shortage in workers for the plantations. There's one thing that seems more like fantasy, but Brazilian teachers say that the Japanese were promised a "land of opportunity", a "golden land", and so on. Just like the Italians that I will describe below, they received low salaries and a long working hours.
Now, I also know a little a bit about the Italians. Just like the Japanese, they were invited to this "land of opportunity", by a treaty signed between Brazil and Italy. (Some italians also immigrated before that treaty, when Italy was not unified) However, when they came, they didn't have a proper home, nor salary. So, they decided to go back. In another round, the Brazilian government invited italians again, now with the "Hospedaria do Imigrante", to give them a temporary home. Salaries continued low, but some continued settled in Brazil.
Basically, Brazil received a lot of immigrants before and after the slavery was abolished.
Now, some sources: Museum of Immigration
Wikipedia sources: Japanese Brazilian Italian Brazilian
You might learn more about immigration on the Museum of Immigration site. ;)