ANSI encoding is a slightly generic term used to refer to the standard code page on a system, usually Windows. It is more properly referred to as Windows-1252 on Western/U.S. systems. (It can represent certain other Windows code pages on other systems.) This is essentially an extension of the ASCII character set in that it includes all the ASCII characters with an additional 128 character codes. This difference is due to the fact that “ANSI” encoding is 8-bit rather than 7-bit as ASCII is (ASCII is almost always encoded nowadays as 8-bit bytes with the MSB set to 0). See the article for an explanation of why this encoding is usually referred to as ANSI.
The name “ANSI” is a misnomer, since it doesn’t correspond to any actual ANSI standard, but the name has stuck. ANSI is not the same as UTF-8.
Technically, ANSI should be the same as US-ASCII. It refers to the ANSI X3.4 standard, which is simply the ANSI organisation’s ratified version of ASCII. Use of the top-bit-set characters is not defined in ASCII/ANSI as it is a 7-bit character set.
However years of misuse of the term by the DOS and subsequently Windows community has left its practical meaning as “the system codepage of whatever machine is being used”. The system codepage is also sometimes known as ‘mbcs’, since on East Asian systems that can be a multiple-byte-per-character encoding. Some code pages can even use top-bit-clear bytes as trailing bytes in a multibyte sequence, so it’s not even strict compatible with plain ASCII… but even then, it’s still called “ANSI”.
On US and Western European default settings, “ANSI” maps to Windows code page 1252. This is not the same as ISO-8859-1 (although it is quite similar). On other machines it could be anything else at all. This makes “ANSI” utterly useless as an external encoding identifier.