A supply-side platform (SSP) is a software system that allows publishers to offer their available inventory to ad exchanges and demand-side platforms (DSP)s. In this context, supply side refers to the supply of advertising space, which is what the publisher is offering. The publisher is typically a website owner but could also be an app developer.
SSPs and DSPs are two entities involved in programmatic advertising, which automates processes around purchase and placement of ads through real-time bidding (RTB). Based on criteria established by advertisers and publishers, such as channels, audience characteristics and purchase options, RTB makes it possible for impressions to be offered and bid on and the winning ad placed, all in the time it takes for a user-requested page to load.
A demand-side platform (DSP), the counterpart to the SSP, is software that allows an advertiser to buy inventory from ad exchanges and manage advertising campaigns.
The Internet Advertising Bureau provides an introduction to how real-time bidding works: