A Squish is a platonic crush, where one strongly desires to be close to a particular individual, but not in a romantic way. It is defined as the desire to be close friends with a particular individual, or to become closer friends with a particular individual if one is already friends with them.
Having squishes is not the same as a general "desire for friends". A squish is targeted towards a specific individual. One can desire friends without feeling squishes. Someone who does not experience squishes may call themself aplatonic.
The term, squish, has been around since at least 2009 (in reference to a platonic crush). It is unknown when it was exactly coined or first started in usage.