Here, I think I know what might be throwing you off - the sort of general common sense one acquires is that mass is something only particles ('matter') have.
Mass is intuitively understood here as one of the things that cause gravity (other being stress and momentum, but these are not important here), and the thing that resists changes in motion (inertia).
The first thing to realize is that mass as described above and energy are the same thing. One might just as well use the two interchangeably.
The second thing to realize is that mass=energy is not only a property of particles, but also of their arrangement and motion.
The last thing needed is that there is a property some particles have called 'rest mass', which is the energy 'encoded' in an isolated, motionless particle. This rest mass is just one of the components of the gravitational and inertial mass/energy described above. So as not to confuse mass and rest mass, it's best to stick to calling the former one energy (we'll do that from now on).
Now, let's take U-235 fission process (the first step only), where it spontaneously decays into a thorium-231 nucleus and an alpha particle.
The total energy (remember, that's the conventional idea of what 'mass' is) of a U-235 nucleus, ##E_{total}## is the sum of rest masses of its nucleons:
$$m_{U235, rest, total} = 92*m_{rest, proton} + 143*m_{rest, neutron}$$
plus their binding energy ##E_{binding}##. Binding energy in attractive potential is negative, so adding it makes the ##E_{total}## lower. The more tightly bound the nucleus, the more negative the energy.
So, the total energy balance in the fusion reaction is:
$$(m_{U235, rest, total} + E_{binding, U235}) = (m_{Th231, rest, total} + E_{binding, Th231}) + (m_{alpha, rest, total} + E_{binding, alpha}) + E_{released}$$
Where the rest energies of all components (protons+neutrons) of U235 equal the sum of rest energies of components of Th231 and the alpha particle (which is made of 2 protons and 2 neutrons). That is to say, both sides of the equation have the same number of protons and the same number of neutrons.
But the energy of U235 is reduced by its binding energy ##E_{binding, U235}##, which is less negative than the sum of binding energies of Thorium-231 and the alpha particle:
$$E_{binding, U235}>E_{binding, Th231} + E_{binding, alpha}$$
(remember higher binding energy means less negative)
The excess energy coming from the difference shown above is the released energy, or in other words - the mass defect. That energy is the missing mass.
