Brazilian wandering spider is the name used to describe any spider of the genus phoneutria. There are five in total, and they are large hairy spindly-looking spiders with leg-spans which can reach up to 5 inches or more. Two pairs of their eight eyes are large, and they do not make webs, instead go hunting for prey. This can cause problems, as they have the most active venom of any living spiders. One of their number, the Brazilian Huntsman, is thought to be the most venomous spider in the world. Brazilian wandering spiders are certainly dangerous, bite more people than any other spiders. They are fast-moving, their legs are strong and spiny and they have destinctive red jaws which they display when angered. These spiders are quite capable of jumping onto a broom used to fend them off, can also leap out of banana bunches carried over the shoulder and bite whoever is carrying the fruit. One species, the Brazilian Armed Spider, is quite amazingly aggressive and has the largest venom glands of any spider. Since the introduction of anti-toxins, there have been few recorded fatalities, and finding one of these spiders in imported fruit is unlikely what with modern safety precautions. the name Brazilian wandering spider is actually inaccurate, as these spiders are found all over South America.
It's worth pointing out that a Brazilian wandering spider is not a tarantula. They're not even in the same family group. Tarantulas are harmless to humans, are mostly ambush killers who wait for prey to come to them. Brazilian wandering spiders are active hunters. Brazilian wandering spiders and tarantulas do have one thing in common, however. They don't eat bananas. I'm quite amazed people think this is the case.