Wiktionary
n. A genre of music which uses rock instrumentation for "non-rock" purposes, often producing songs which are akin to rock music, yet still very different.
Wikipedia
Post-rock is a subgenre of rock music characterized by the influence and use of instruments commonly associated with rock, but using rhythms and "guitars as facilitators of timbre and textures" not traditionally found in rock. Post-rock bands are often instrumental.
Sigur Rós, Explosions in the Sky, Stereolab, Mogwai, Don Caballero and Tortoise are among the more prominent bands described as post-rock, but their styles are very different, despite being instrumental bands centered on guitars and drums. As such, the term has been the subject of backlash from listeners and artists alike.
Although firmly rooted in the indie or underground scene of the 1980s and early 1990s, post-rock's style often bears little resemblance musically to that of contemporary indie rock.