Texture stitching takes all the small texture files from all mods and combines them into one big texture sheet (see below). If every texture would be uploaded to the graphics card on it's own, the graphics card would not be very happy about that.
Model baking is taking the models that are specified in JSON or other formats and turning them into an efficient and compact format to be used during actual rendering of the models.
These things happen twice (the first round they actually work on dummy values to speed things up), due to the way Minecraft is designed. At startup the game runs these things once, but then forge loads mods which add textures and models, so the process has to happen again.