AES
NIST block cipher. 128-bit blocks, keys of 128, 192, or 256 bits. The algorithm is solved. Mode and key handling are the work.
AES is the Advanced Encryption Standard. NIST selected the Rijndael family in 2000 and published it as FIPS 197 in 2001 (updated May 2023 with no change to the algorithm). It is a symmetric block cipher: the same secret key encrypts and decrypts. Blocks are 128 bits. The suffix is the key length: AES-128, AES-192, AES-256.
AES is the engine. The mode is the vehicle. Electronic codebook (ECB) repeats patterns in the ciphertext. You want an authenticated mode, usually GCM, so you get confidentiality and a tag that the ciphertext was not cut-and-pasted. At rest, that is disk or application encryption with keys the host cannot casually unwrap. In transit, TLS 1.3 is what puts AES-GCM on the wire for you.
A 256-bit key does not rescue a key in the same database as the data, a home-rolled wrapping scheme, or a library you compiled from a blog. Use a current crypto library, store keys in a KMS or HSM, and rotate. AES is what you use for bulk data. It is not a substitute for TLS, and it is not homomorphic: whoever holds the key can read the lot.
Fact source: NIST FIPS 197, AES.