Neutron reactions with nuclei
You will find a discussion of this in this same forum -(Neutron Capture) cross-section.
Slow neutrons tend to react with most nuclei, though with varying ease. Being uncharged, they are not repelled by the nuclei, and just as it easier to catch a slow-moving ball than a fast one, a slow neuton is more easily captured than a fast one.
Fast neutrons are needed when the reaction is one which absorbs energy, which must therefore be provided by the fast neutron, e.g the breakup of a light nucleus. For example Be-9 + n ---> 2He-4 + 2n absorbs energy, so fast neutrons must be used.
Other reactions needing fast neutrons are those with high activation energies, such as the fission of common uranium (U-238). This merely absorbs slow neutrons and does not break up - it produces U-239 which then beta-decays in two steps tp Pu-239. Note that U-238 has an even number of neutrons, and addition of a neutron when there is already an even number releases relatively little energy, so the resulting nucleus is not 'shaken up' much. (Again see post on neutron cross-sections.) However fast neutrons will fission U-238, the energy they bring with them disturbs the nucleus enough to provoke fission.
Pu-239, and also U-233 and U-235, do fission with slow neutrons. Note all these nuclei have odd numbers of neutrons. The addition of another releases much energy, enough to 'shake up' the nucleus so that it fissions.
Hope this helps!