I've read that particles in nuclear fission disintegrates into two particles with higher binding energy, and in this process energy is released. Now I am just trying to understand this by common sense, but I am not able to. Because the particle with lower binding energy makes particles of total net higher binding energy, meaning that it takes more energy for the particles with higher binding energy to be formed from the particle with lower binding energy. Hence, shouldn't energy actually be absorbed in this process? Could someone explain where is my reasoning wrong?
To make an atom of, say, uranium-235, you have to squeeze the protons and neutrons together with tremendous force to get all of them to stick together (just barely). In so doing, you are storing energy in that nucleus and it is then like a cocked mouse trap, waiting for something to trigger it and release that stored energy.
The trigger takes the form of a speeding neutron which fractures the nucleus and releases the stored energy.
The resulting fragments are far less unstable than the uranium nucleus was. "Less unstable" means the protons and neutrons in those "daughter nuclei" are hanging onto one another more tightly, which means their binding energy per nucleon is greater. As pointed out by Jon Custer, those fragments have sunk deeper into the potential energy well; this means to split one of them would release little or no additional energy.
In an accounting of the energy content of a nucleus, the binding energy is negative. When people talk about a "larger binding energy," they are referring to the magnitude of the binding energy. When a massive system goes from small (negative) binding energy to large (negative) binding energy, the masses of its constituents stay the same, but its total energy decreases.