Antimatter is a particle physics term referring to material composed of antiparticles. In Assassination Classroom, it serves as the main reason behind the tentacle cells.
In Particle Physics
Antimatter is formed of antiparticles which have the same mass as particles but with opposite charge. For example while a proton has a positive charge, an antiproton has a negative charge, and while an electron has a negative charge, a positron(antiparticle of electron) has a positive charge.
Like how an electron and a proton form a Hydrogen atom, an antiproton and a positron can form an Antihydrogen atom. Antimatter in form of anti-atoms is extremely difficult to produce, but anti-particles can be produced by particles accelerators. If antimatter and matter encounter each other, both will be annihilated and there will be energy given out during the process in accord with the equation E = mc2 .
In the series, antimatter is what Yanagisawa's research is for. In order to create a new source of energy, Yanagisawa secretly led some scientists studying a method to make antimatter grow in a human's body.
Korosensei (The former god of death) became a guinea pig for this experiment, he had antimatter generating cells implanted in his body which will continuously produce antimatter as long a he's alive. However, after Yanagisawa learned that in the moment the cell division stops, the antimatter generation cycle will continue and finally lead to devastating chain reaction, he decided to kill Korosensei before the destruction of the earth caused by a reaction once his cell division stops.