Properties provided by GCM In the introduction of NIST Special Publication 800-38D is said that:


  GCM provides assurance of the confidentiality of data using a variation of the Counter mode of operation  for  encryption. GCM  provides  assurance  of  the  authenticity  of  the  confidential  data  (up to about 64 gigabytes per invocation) using a universal hash function that is defined over a binary  Galois  (i.e.,  finite)  field.    GCM  can  also  provide  authentication  assurance  for  additional data (of practically unlimited length per invocation) that is not encrypted.


As a block cipher GCM guarantees the confidentiality of data, but what does it mean that it assures its authenticity?
And what is exactly the authentication assurance for the unencrypted additional data?

I believe that data authenticity may correspond to its integrity, i.e. the absence of tamperings, while I'm not sure of the meaning of the authentication for the additional data.
Authenticity of the data assures that the data in question was created or modified by an authorized party (a key holder). Without authenticity, anyone could present an arbitrary block of data as a valid ciphertext. Though it is overwhelmingly likely that decrypting such a block will result in a garbage plaintext, it can still disrupt the application that is attempting to use the data. This is different from integrity, in that integrity assures you that a given piece of data has not been modified (either by an unauthorized party or by more mundane sources of data corruption such as bad hardware/line noise/cosmic rays/etc).


  So the authentication of the additional data corresponds only to the property that it is received in the same condition that it was sent out, without modifications? 


Technically, integrity is what guarantees that the data was received in the same condition as it was sent out. Authenticity assures that the data originated from an authorized party. 

Integrity can be seen as a subset of Authenticity. For example, you can obtain integrity by hashing a message. This does not provide authenticity though. For that, you require a MAC.