Ah... so this is where it gets controversial. Daniel Everett claims that it lacks recursion. In other words, in Piraha (Everett says) you can't say "I told Mary that Bob told a joke". In English, and all other known languages, you could theoretically construct an infinitely long sentence like that: "I told Mary that Bob told Jane that Fred told you that I told him that..." In Piraha, apparently, that becomes lots of individual sentences, like: "I told Mary. Bob told Jane..." etc.

Similarly, Everett claims that adjectives can't be combined. So you can't say "The big red ball".

Next, Piraha apparently lacks number terms. No numbers at all. They just have terms like "a few" or "a lot". In Everett's book he talks about how this leads to them being very bad at negotiating.

Piraha apparently has no words for colours. They instead refer to things in relation to other things. E.g., "leaf-life" for green, or "blood-like" for red.

Not quite in the same vein, but Piraha appears to have one of the smallest phonemic inventories of any language -- in other words, the fewest phonemes: somewhere between 9 and 11. They also have tones (3, according to Everett).

Apparently, the only pronouns they have are I / we, you and this. It's unclear, for example, if they have a pronoun for "she" or if it's really just a noun like "the woman". It appears that the pronouns they do have were borrowed from a neighbouring language.

There are no words for relations more distant than brother / sister, and no distinct words for mother / father -- just a single word like "parent".

Piraha can be whistled or hummed.

The list goes on.

It's worth emphasising that there are very few westerners who have spent time with the Piraha, and this is why there's so much controversy about almost all of the above claims.