Why a slow moving neutron is required in nuclear plants? I came across a line that said "an atom of heavy element is hit with a low velocity neutron, otherwise the required reaction would not achieve result". So, why not a neutron of high velocity is successful to achieve a nuclear fission ?  
 A: The cross section for neutron absorption is dependent on the energy ("velocity", "temperature") of the neutron. Graph from Nuclear reactions [Los Alamos National Laboratory], regarding the energy dependence of the neutron absorption cross section for $^{235}\mathrm{U}$:

Note the logarithmic scales. Neutrons emitted from the fission reactions are in the order of $\mathrm{MeV}$, but are moderated down towards the "thermal" region (${\sim}0.025\,\mathrm{eV}$) in nuclear reactors, which yields a cross section about three orders of magnitude larger than fast neutrons, as seen in the graph above. That is the meaning of your text, though "why?" is often an extremely complicated question in these contexts, depending on what one means.
The "reason" is contained within the laws of quantum mechanics. The absorption of a neutron can be modeled crudely by looking at the transmission probability for the neutron to penetrate a rectangular potential barrier, which for low-energy neutrons yields a $1/v$ dependence of the absorption where $v$ is the neutron velocity, which corresponds quite well to the initial part of of the absorption graph above. In the middle of the spectrum we reach resonances and further complications though.
We can try to create mental images with somewhat intuitive analogues, but they will mostly be based on "after the fact"-type of arguments; e.g., for another near-lying isotope such as $^{238}\mathrm{U}$, there is no (at least to a vanishingly small probability) fission at all in the thermal region, and then we need to have fast neutrons for fission to occur, so there are a lot of variables in play (excitation energy of the resulting configuration, activation energy to overcome the potential barrier, etc.). This also makes your quote regarding a "heavy element" a bit too general.
The above graph is what we measure — we have to accept it, and design our nuclear reactors with this in mind. That is probably the best answer to "why?" I can produce. :-)
