The American National Standards Institute is a private organisation that collaborates with government and non-government entities to create technical standards.
One example that many programmers will have encountered is the ASCII character set, which was a huge improvement over the vast number of different manufacturer encodings in use beforehand (of which only IBM's EBCDIC has survived in any meaningful way).
Also significant because, ANSI escape codes are used to control text formatting and other output options on text terminals.
ANSI C or ISO C or Standard C, refers to the C language specifications the superseded the original K&R C.