Yarn can be seen as the distributed operating system of Hadoop where all apps are build on top of it.
Image comes from Hortonworks
YARN was originally proposed (MR-279) and architected by one of the HortonWorks founders, Arun Murthy.
Yarn is the NextGen MapReduce (2.x). It maintains API compatibility with previous stable release (hadoop-1.x). All application should still run unchanged on top of YARN with just a recompile.
Yarn is able to run map reduce application but it is also possible to write other types of applications (having nothing to do with MapReduce). See Yarn - Application (app)
Hadoop YARN is part of Hadoop core and has as leader component the resource Manager. See Yarn - Architecture / Topology / Components