In GCM, the 'C' is for counter, and hence turning AES into a stream cipher. This part is usually known as 'AES-CTR'. The 'G' is Galois for 'Galois field multiplication', which allows for a parallelizable way of computing a MAC. AES-GCM packages AES-CTR (a stream cipher made from a block cipher) and GMAC (the Galois MAC) together into a primitive. This type of scheme, which combines confidentiality, integrity, and authenticity is called 'authenticated encryption with associated data' (AEAD) [1]. A stream cipher is the easiest way of accomplishing that the cipherstream will safely expand to cover all the plaintext.

Other famous AEAD schemes are:

- CCM (Counter with CBC-MAC), packages AES-CTR and CBC-MAC together in an authenticate-then-encrypt regime

- ChaCha20-Poly1305, which packages together the stream cipher ChaCha20 and the MAC Poly1305.

[1] https://en.wikipedia.org/wiki/Authenticated_encryption

The AES-GCM mode of operation turns the AES block cipher into a stream cipher. Doing this makes it possible to add authentication on top for relatively cheap. The ChaCha20-poly1305 has a similar construction. These are the two most secure and efficient ciphers available in TLS, so they get a lot of use. If you are sending documents over HTTPS, you definitely want them encrypted with one of these two.

Why wouldn't you?