At some point prior to the events of Invader Zim: Enter the Florpus, Zim attempted to create a clone of Professor Membrane who could then take his place and ground Dib forever.
However, Zim considered the clone a failure - not because he barely looks like Membrane and doesn't act like him, but because he failed to teach him how to make pudding the way that Zim believes Dib loves. Because of this, he locked the clone away in a pod, only letting him out while searching through his experiments for something to use in Phase 2 of his newest plan.
After kidnapping Professor Membrane and locking him away on Moo-Ping 10, Zim finally makes use of the clone, having him keep Dib and Gaz under effective house arrest; it's during this point that Gaz gives the clone the name Clembrane (shorthand for "Clone Membrane"). Eventually, however, they manage to convince Clembrane to let them fix up Tak's Ship, which they then use to fly to Moo-Ping 10 to save their father, while leaving Clembrane behind.
Later, during the film's climatic fight, Clembrane arrives on the scene, where he fights the real Membrane, whom he's convinced is the imposter. During the fight, Clembrane gets ahold of Minimoose, who the Membranes need to reverse Zim's transportation of Earth and send it back to its proper place. Zim tries to convince him to hand Minimoose over and destroy the Membranes, but as he believes that they're his family, Clembrane refuses, instead giving them Minimoose and restraining Zim as the Professor saves the planet.
Afterwards, Clembrane is shown having dinner with the Membranes, with Dib questioning if he lives with them now.
Appearance
Clembrane wears the same lab coat outfit as Professor Membrane and has the same scythe hairstyle, but beyond that they look completely different. Clembrane is taller, and much more bloated than the Professor, his head being swollen and orange, with a stitch-mark in the middle of his face.
Also, his eyes are visible and always open (as opposed to Membrane, who always covers his eyes with goggles), and his left hand is much larger than his right. He also has a small hump on his back.
Clembrane also has a slight resemblance to Nightmare Dib as he had the same lobotomy scar on his forehead and a similar big head and mouth.
Personality
Clembrane is very upbeat and happy, albeit very overbearing. As he's convinced that he's the real Professor Membrane, he genuinely cares about Dib and Gaz, wanting to spend time with them and even being willing to turn on Zim to protect them.
Clembrane is so convinced that he's the real Membrane that if anyone tells him otherwise he throws a massive tantrum, rolling around and smashing everything in sight.
Also, Clembrane is obsessed with pudding. He's constantly shown making it, and serves it to Dib and Gaz at every opportunity.
In contrast to his genetic template Professor Membrane, Clembrane lacks intelligence but is still a formidable fighter and seems to have the ability to move inhumanly fast, both abilities that he used repeatedly to care for Dib and Gaz.
Facts of Doom
Clembrane's preliminary designs by Aaron Alexovich.
Aaron Alexovich said he went in some wild directions when he first started to design Clembrane.
Justin Roiland was meant to be Clembrane's voice actor, with Jhonen Vasquez providing the current voice as a placeholder, as Roiland had a busy schedule and they weren't sure if they could get him. They eventually got him for the movie, but the crew had all fallen in love with Vasquez's Clembrane voice by then, so instead Roiland was relegated to the role of Foodio 3000.
Clembrane's creation is ironic, as there was meant to be an episode prior to the series' cancelation in which Dib was to discover that he was a clone created by his father.
The fact that he is a (failed) clone of Professor Membrane heavily implies that Zim somehow got his DNA in order for the cloning process to be made possible.
Clembrane is the second Nicktoon clone created by a villain as a means to take care of the hero for the purpose of an evil plan, the first is Dani Phantom who is a female clone of Danny Phantom created by Vlad Plasmius.
Ironically despite having an obsession with pudding, Clembrane was only once seen eating pudding during the film's climax.
