Definition
AES on its own encrypts single 128-bit blocks, so it needs a 'mode of operation' to handle real traffic. GCM, specified by NIST in SP 800-38D, turns AES into a stream-like cipher with a built-in integrity tag. AES-256-GCM is the most common setting in VPN marketing.
How it works
Counter mode encrypts a running counter and XORs the result with the data, which can be done in parallel. GHASH, a fast multiplication over a finite field, then produces an authentication tag. Modern CPUs have AES and carry-less multiply instructions, so AES-GCM is very fast on laptops and recent phones.
Why it matters
AES-GCM is the default data cipher in OpenVPN 2.4 and later, in IKEv2/IPsec setups and in TLS 1.3. It replaced older AES-CBC plus HMAC combinations because it is faster and harder to misconfigure. The main rule: a nonce must never repeat under the same key.