The Free On-line Dictionary of Computing (30 December 2018):

application service provider

    (ASP) A service (usually a business)
   that provides remote access to an application program across
   a network protocol, typically HTTP.  A common example is
   a website that other websites use for accepting payment by
   credit card as part of their online ordering systems.

   As this term is complex-sounding but vague, it is widely used
   by marketroids who want to avoid being specific and clear at
   all costs.

   (2001-03-26)