DSP stands for Demand Side Platform -- it's basically a supply aggregation platform that advertisers can use to buy ad inventory programmatically. A DSP connects to ad exchanges and allows advertisers to set some bid guidelines (like targeting parameters, bids, etc.) and have impressions be purchased programmatically from ad exchanges on a real-time bidding basis. There are a number of great resources available that explain how DSPs work in detail, so I won't elaborate further.
Since most of the people on QuantMar operate on mobile, I think it's more interesting to discuss how the role of DSPs in the mobile ecosystem is changing as of 2019. The reality is that DSPs weren't really relevant for app advertisers until a few years ago -- or, at least, they weren't visible to most mobile marketers that primarily buy in-app ad inventory. A mobile marketing team easily could have operated at scale in eg. 2014 without ever interacting directly with a DSP.
I gave a presentation recently called The State of the App Economy: 2019 and beyond in which I talk about the paradigm shift that has taken place within mobile marketing in past 1-2 years with spend being shifted into algorithmic campaign management on Facebook and Google and the "Tier 2" networks losing market share (or at least not participating in market growth). By "networks" here I mean the companies that offer SDK traffic: where publishers integrate network SDKs into their apps and the networks act as brokers, connecting advertisers with their publishers' traffic. Consolidation in the space has drastically reduced the number of legitimate, important SDK ad networks.
But back in the 2012-2015 era of mobile advertising, when Facebook and Google might only account for 20% of any given advertiser's spend, a plethora of networks existed that connected publishers to advertisers. In effect, these in-app ad networks are DSPs: they aggregate supply (their own in-app SDK traffic) and provide an interface for advertisers to target that supply and buy it programmatically (some networks are / were more sophisticated than others, but the large ones now all offer self-serve interfaces). Buying in-app inventory from exchanges in that period wasn't very common; there was no need to use a DSP if networks provided the same functionality and had better access to in-app inventory.
But we live in a new era of mobile marketing, with Facebook and Google capturing almost all growth in mobile advertising revenue and moving advertisers into event-based, algorithmic campaign structures like AEO, VO, and UAC. Most large app advertisers are spending 50%+ of their budgets on these two channels now, and programmatic has emerged as a means of diversifying a traffic portfolio. With this growth of programmatic buying on mobile, DSPs are suddenly relevant to mobile marketing teams: they are the interface through which teams buy inventory on exchanges. Additionally, more in-app inventory is available on exchanges now (partly due to growth in the hypercasual gaming category and rich video and playable ads creating significant revenue opportunities for mobile games developers), and the larger ad networks have all created their own DSPs to facilitate programmatic buying.