Standip is the incestuous shipping of Stanley Pines and Dipper Pines.
Over the course of the series, Dipper and Stan have developed a very close relationship. They are similar in the regards that they care very deeply for their family, putting the happiness of their family over their own. However, both have questionable moral standards, doing what is not necessarily 'the right thing' to get ahead or get their way.
Seeing as Stan is a man of questionable morals, some fans of the ship see Stan pursuing a taboo sexual relationship with Dipper (who may not reciprocate at first, or at all). Dipper may also be portrayed instigating this relationship out of pubescent curiosity or a desire to become 'closer' to his great uncle. This ship is much more sexual in nature in comparison to its counterpart, Stanbel.
Standip can also go hand-in-hand with Stancest. Stan could see his brother, Stanford, in the dorky, headstrong, anxious Dipper and thus desire a sexual relationship with him in order to fill the gap that Stanford left. Whether Stan's incestuous feelings for his brother are one-sided or reciprocated are entirely up to the shippers.