Dot is a tesseract, a four-dimensional hypercube, accompaning Gomez in his travel.
After you obtain your fez from Geezer , Dot is sent to guide you. Dot gives you helpful tips and guidelines throughout the game. Dot is believed to be a reference to Navi from the 'The Legend of Zelda' saga, sometimes even referencing the line "Hey, listen". Dot also acts as a light source in some of the darker levels.