What it actually does
A demand-side platform sits on the buyer's side of an automated marketplace. When an impression becomes available — a page loading, a stream starting — the platform decides in roughly a hundred milliseconds whether to bid on it and how much, based on the audience, the placement and the rules you set. Multiply that by billions of decisions and you have programmatic buying.
The value proposition is aggregation. Rather than negotiating with fifty publishers, you set an audience and a budget once and the platform sources inventory across all of them. That is genuinely useful, and it is why programmatic took the share of digital advertising that it did.
What it is not is a source of inventory. A DSP owns nothing. It buys from supply-side platforms and exchanges, which is the fact that explains the fee structure underneath it.