Gzip is any of several software applications used for file compression and decompression. The term usually refers to the GNU Project's implementation, "gzip" standing for GNU zip. It is based on the DEFLATE algorithm, which is a combination of Lempel-Ziv (LZ77) and Huffman coding. The program was created by Jean-Loup Gailly and Mark Adler as a free software replacement for the compress program used in early Unix systems, and intended for use by the Project. Version 0.1 was first publicly released on October 30, 1992, and version 1.0 followed in February 1993.
OpenBSD's version of gzip is actually the compress program, to which support for the gzip format was added in OpenBSD 3.4. The 'g' in this specific version stands for gratis.
FreeBSD, DragonFlyBSD and NetBSD use a BSD-licensed implementation instead of the GNU version; it is actually a command-line interface for zlib intended to be compatible with the GNU implementation's options. These implementations originally come from NetBSD, and supports decompression of bzip2 and Unix pack(1) format.