It's a neat trick of projection, and really easy to hack on and extend yourself once you know the trick. Using your map of the space, cast a ray from the camera position through every column of the display rectangle; using the distance the ray travelled before intersecting the wall, you can calculate the apparent height of the wall seen in that column of the display; so, in that column, draw the wall that high. You can get fancier with textures for the walls, varying the floor height, walls that can appear and disappear (i.e. "doors"), and so on.

Better than my 10-second explanation: https://lodev.org/cgtutor/raycasting.html