He is made of ghost energy and coffee.
Gooigi is often described as being made of just ectoplasma but, scientifically speaking, he's actually made of "goo." Goo was discovered by Professor E. Gadd during an accident in his lab. While he was experimenting with "strange liquid ghost energy" a ghost startled him, causing him to spill his coffee into the ghost energy. Specifically, the coffee was "a Lunoman Greenie blend from Evershade" all of which is carefully documented in Professor E. Gadd's research journal. The result was a somewhat viscous green element called goo which eventually was used to make Gooigi.
His appearance comes from Luigi's biological data.
Professor E. Gadd made Gooigi in Luigi's image because he needed it to take a human form so it could be trained/made into in a ghost-catching machine to help with E. Gadd's research. E.Gadd used "the biological data that the Pixelator captured when Luigi used it" to collect this DNA and put it into what would become Gooigi.
He's a time traveler.
Professor E. Gadd created Gooigi sometime during or after the events of Luigi's Mansion Dark Moon. He wanted Gooigi to have a place to practice catching ghosts so he sent him back in time to the first Luigi's Mansion game.
He watched hours of Luigi footage.
To teach Gooigi how to catch ghosts for him, E. Gadd made him watch "vast amount of footage of Luigi doing exactly that." After a while, the Goo began to mimic Luigi's movements—he even transformed a part of his body into a perfect replication of the Poltergust."
He can walk over spikes and slip through bars.
Due to his goo properties, Gooigi can walk across spikes unharmed and slip through small spaces such as bars.
He can be destroyed with fire and water.
Because he is made of goo, Gooigi can be destroyed with fire and water. This is why we see him melt into the drain in the extended gameplay trailer. When he came into contact with water, he lost his form.
Gooigi and Luigi have a strange, direct connection.
During the multiplayer footage, Luigi and Gooigi move on screen at the same time. But during the single-player footage we see Luigi slumped over, as if lifeless, when Gooigi appears on screen. This suggests they may be more connected than anyone could've hoped. When asked about this bizarre phenomenon JC Rodrigo, manager of product and marketing, said in these moments of the game Luigi is "sort of drifting." Somehow, that's even scarier.
