In the demoscene, this term refers to the early days of the scene. For the PC scene, those were the late 80's, early 90's. It's also used to describe the demos of that time, the sceners who made them, and modern demos that follow the same style.
From an artistic point of view, oldskool demos suck badly. The visual effects use at most 256 colors, in a low resolution which look very blocky on your modern 21 inch monitor, the modular music uses crackling 8-bit samples, and the 3D scenes, if any, don't show anything more complex than a spinning cube. But because it took a lot of skill to create a realtime demo on such slow hardware, and because they often contained funny or provoking messages, many sceners think of them with nostalgia. For them, oldskool is a term of respect.