We know that Noach also conversed with the raven and the dove in the Ark.
In addition, other very special Sages throughout the ages (like King Shlomo & the Arizal) merited the ability to understand what birds say.
Yet we also know that birds can't think like we do. And speech is a uniquely human gift.
So how can we understand these references to conversations with birds?
2 Ways to Understand Birds
(1) Bird communication doesn't consist of actual language, according to the Yad Ramah (Rav Meir Abulafia). Instead, the bird makes certain signs that indicate its intentions.
Probably tweets, chirps, and physical movements comprise those signs. And Noach (among others) possessed the level of prophecy & wisdom necessary to interpret these signs. That's the explanation of the Yad Ramah.
(2) You don't speak to the actual bird, explains the Arizal. Instead, you converse with the bird's sar or upper mazal.
These refer to an angelic force appointed over the bird. I suppose it's like when you visit a home with a pet. In order to fully understand the pet, you let its owner explain the pet's mannerisms & what these mannerisms convey even as you pet & speak to the pet.
Needless to say, speaking to a bird's sar or upper mazal also demands a very high spiritual level of wisdom & merit.
Perhaps there are other explanations, but these are the two I came across.
Hopefully, that sheds some light on the intriguing phenomenon of understanding the language of birds.